Trait Sub

1.0.0 · Source
pub trait Sub<Rhs = Self> {
    type Output;

    // Required method
    fn sub(self, rhs: Rhs) -> Self::Output;
}
Expand description

The subtraction operator -.

Note that Rhs is Self by default, but this is not mandatory. For example, std::time::SystemTime implements Sub<Duration>, which permits operations of the form SystemTime = SystemTime - Duration.

§Examples

§Subtractable points

use std::ops::Sub;

#[derive(Debug, Copy, Clone, PartialEq)]
struct Point {
    x: i32,
    y: i32,
}

impl Sub for Point {
    type Output = Self;

    fn sub(self, other: Self) -> Self::Output {
        Self {
            x: self.x - other.x,
            y: self.y - other.y,
        }
    }
}

assert_eq!(Point { x: 3, y: 3 } - Point { x: 2, y: 3 },
           Point { x: 1, y: 0 });

§Implementing Sub with generics

Here is an example of the same Point struct implementing the Sub trait using generics.

use std::ops::Sub;

#[derive(Debug, PartialEq)]
struct Point<T> {
    x: T,
    y: T,
}

// Notice that the implementation uses the associated type `Output`.
impl<T: Sub<Output = T>> Sub for Point<T> {
    type Output = Self;

    fn sub(self, other: Self) -> Self::Output {
        Point {
            x: self.x - other.x,
            y: self.y - other.y,
        }
    }
}

assert_eq!(Point { x: 2, y: 3 } - Point { x: 1, y: 0 },
           Point { x: 1, y: 3 });

Required Associated Types§

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type Output

The resulting type after applying the - operator.

Required Methods§

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fn sub(self, rhs: Rhs) -> Self::Output

Performs the - operation.

§Example
assert_eq!(12 - 1, 11);

Trait Implementations§

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impl<E> Metrics<dyn Sub<Field<E>, Output = Field<E>>> for Field<E>
where E: Environment,

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type Case = (Mode, Mode)

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fn count( _case: &<Field<E> as Metrics<dyn Sub<Field<E>, Output = Field<E>>>>::Case, ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.
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impl<E> Metrics<dyn Sub<Group<E>, Output = Group<E>>> for Group<E>
where E: Environment,

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type Case = (Mode, Mode)

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fn count( case: &<Group<E> as Metrics<dyn Sub<Group<E>, Output = Group<E>>>>::Case, ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.
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impl<E, I> Metrics<dyn Sub<Integer<E, I>, Output = Integer<E, I>>> for Integer<E, I>
where E: Environment, I: IntegerType,

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type Case = (Mode, Mode)

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fn count( case: &<Integer<E, I> as Metrics<dyn Sub<Integer<E, I>, Output = Integer<E, I>>>>::Case, ) -> Count

Returns the number of constants, public inputs, private inputs, and constraints.
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impl<E> OutputMode<dyn Sub<Field<E>, Output = Field<E>>> for Field<E>
where E: Environment,

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type Case = (CircuitType<Field<E>>, CircuitType<Field<E>>)

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fn output_mode( case: &<Field<E> as OutputMode<dyn Sub<Field<E>, Output = Field<E>>>>::Case, ) -> Mode

Returns the mode of the output.
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impl<E> OutputMode<dyn Sub<Group<E>, Output = Group<E>>> for Group<E>
where E: Environment,

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type Case = (Mode, Mode)

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fn output_mode( case: &<Group<E> as OutputMode<dyn Sub<Group<E>, Output = Group<E>>>>::Case, ) -> Mode

Returns the mode of the output.
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impl<E, I> OutputMode<dyn Sub<Integer<E, I>, Output = Integer<E, I>>> for Integer<E, I>
where E: Environment, I: IntegerType,

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type Case = (Mode, Mode)

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fn output_mode( case: &<Integer<E, I> as OutputMode<dyn Sub<Integer<E, I>, Output = Integer<E, I>>>>::Case, ) -> Mode

Returns the mode of the output.

Implementors§

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impl Sub for f16

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impl Sub for f32

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impl Sub for f64

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impl Sub for f128

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impl Sub for i8

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impl Sub for i16

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impl Sub for i32

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impl Sub for i64

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impl Sub for i128

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impl Sub for isize

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impl Sub for u8

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impl Sub for u16

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impl Sub for u32

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impl Sub for u64

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impl Sub for u128

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impl Sub for usize

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impl Sub for Assume

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impl Sub for Saturating<i8>

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impl Sub for Saturating<i16>

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impl Sub for Saturating<i32>

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impl Sub for Saturating<i64>

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impl Sub for Saturating<i128>

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impl Sub for Saturating<isize>

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impl Sub for Saturating<u8>

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impl Sub for Saturating<u16>

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impl Sub for Saturating<u32>

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impl Sub for Saturating<u64>

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impl Sub for Saturating<u128>

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impl Sub for Saturating<usize>

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impl Sub for Wrapping<i8>

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impl Sub for Wrapping<i16>

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impl Sub for Wrapping<i32>

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impl Sub for Wrapping<i64>

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impl Sub for Wrapping<i128>

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impl Sub for Wrapping<isize>

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impl Sub for Wrapping<u8>

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impl Sub for Wrapping<u16>

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impl Sub for Wrapping<u32>

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impl Sub for Wrapping<u64>

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impl Sub for Wrapping<u128>

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impl Sub for Wrapping<usize>

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impl Sub for Duration

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impl Sub for Instant

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impl Sub for BigInt

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impl Sub for BigUint

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impl Sub for CreateFlags

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impl Sub for ReadFlags

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impl Sub for WatchFlags

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impl Sub for Access

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impl Sub for AtFlags

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impl Sub for FallocateFlags

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impl Sub for MemfdFlags

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impl Sub for Mode

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impl Sub for OFlags

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impl Sub for RenameFlags

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impl Sub for ResolveFlags

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impl Sub for SealFlags

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impl Sub for StatVfsMountFlags

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impl Sub for DupFlags

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impl Sub for FdFlags

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impl Sub for ReadWriteFlags

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impl Sub for IFlags

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impl Sub for StatxAttributes

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impl Sub for StatxFlags

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impl Sub for XattrFlags

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impl Sub for Timespec

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impl Sub for ATerm

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impl Sub for Z0

Z0 - Z0 = Z0

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impl Sub for UTerm

UTerm - UTerm = UTerm

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impl Sub<&f16> for &f16

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impl Sub<&f16> for f16

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impl Sub<&f32> for &f32

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impl Sub<&f32> for f32

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impl Sub<&f64> for &f64

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impl Sub<&f64> for f64

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impl Sub<&f128> for &f128

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impl Sub<&f128> for f128

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impl Sub<&i8> for &i8

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impl Sub<&i8> for &BigInt

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impl Sub<&i8> for i8

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impl Sub<&i8> for BigInt

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impl Sub<&i16> for &i16

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impl Sub<&i16> for &BigInt

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impl Sub<&i16> for i16

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impl Sub<&i16> for BigInt

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impl Sub<&i32> for &i32

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impl Sub<&i32> for &BigInt

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impl Sub<&i32> for i32

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impl Sub<&i32> for BigInt

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impl Sub<&i64> for &i64

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impl Sub<&i64> for &BigInt

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impl Sub<&i64> for i64

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impl Sub<&i64> for BigInt

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impl Sub<&i128> for &i128

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impl Sub<&i128> for &BigInt

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impl Sub<&i128> for i128

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impl Sub<&i128> for BigInt

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impl Sub<&isize> for &isize

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impl Sub<&isize> for &BigInt

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impl Sub<&isize> for isize

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impl Sub<&isize> for BigInt

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impl Sub<&u8> for &u8

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impl Sub<&u8> for &BigInt

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impl Sub<&u8> for &BigUint

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impl Sub<&u8> for u8

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impl Sub<&u8> for BigInt

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impl Sub<&u8> for BigUint

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impl Sub<&u16> for &u16

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impl Sub<&u16> for &BigInt

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impl Sub<&u16> for &BigUint

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impl Sub<&u16> for u16

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impl Sub<&u16> for BigInt

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impl Sub<&u16> for BigUint

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impl Sub<&u32> for &u32

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impl Sub<&u32> for &BigInt

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impl Sub<&u32> for &BigUint

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impl Sub<&u32> for u32

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impl Sub<&u32> for BigInt

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impl Sub<&u32> for BigUint

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impl Sub<&u64> for &u64

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impl Sub<&u64> for &BigInt

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impl Sub<&u64> for &BigUint

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impl Sub<&u64> for u64

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impl Sub<&u64> for BigInt

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impl Sub<&u64> for BigUint

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impl Sub<&u128> for &u128

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impl Sub<&u128> for &BigInt

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impl Sub<&u128> for &BigUint

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impl Sub<&u128> for u128

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impl Sub<&u128> for BigInt

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impl Sub<&u128> for BigUint

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impl Sub<&usize> for &usize

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impl Sub<&usize> for &BigInt

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impl Sub<&usize> for &BigUint

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impl Sub<&usize> for usize

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impl Sub<&usize> for BigInt

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impl Sub<&usize> for BigUint

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impl Sub<&Saturating<i8>> for &Saturating<i8>

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impl Sub<&Saturating<i8>> for Saturating<i8>

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impl Sub<&Saturating<i16>> for &Saturating<i16>

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impl Sub<&Saturating<i16>> for Saturating<i16>

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impl Sub<&Saturating<i32>> for &Saturating<i32>

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impl Sub<&Saturating<i32>> for Saturating<i32>

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impl Sub<&Saturating<i64>> for &Saturating<i64>

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impl Sub<&Saturating<i64>> for Saturating<i64>

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impl Sub<&Saturating<i128>> for &Saturating<i128>

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impl Sub<&Saturating<i128>> for Saturating<i128>

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impl Sub<&Saturating<isize>> for &Saturating<isize>

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impl Sub<&Saturating<isize>> for Saturating<isize>

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impl Sub<&Saturating<u8>> for &Saturating<u8>

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impl Sub<&Saturating<u8>> for Saturating<u8>

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impl Sub<&Saturating<u16>> for &Saturating<u16>

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impl Sub<&Saturating<u16>> for Saturating<u16>

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impl Sub<&Saturating<u32>> for &Saturating<u32>

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impl Sub<&Saturating<u32>> for Saturating<u32>

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impl Sub<&Saturating<u64>> for &Saturating<u64>

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impl Sub<&Saturating<u64>> for Saturating<u64>

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impl Sub<&Saturating<u128>> for &Saturating<u128>

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impl Sub<&Saturating<u128>> for Saturating<u128>

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impl Sub<&Saturating<usize>> for &Saturating<usize>

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impl Sub<&Saturating<usize>> for Saturating<usize>

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impl Sub<&Wrapping<i8>> for &Wrapping<i8>

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impl Sub<&Wrapping<i8>> for Wrapping<i8>

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impl Sub<&Wrapping<i16>> for &Wrapping<i16>

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impl Sub<&Wrapping<i16>> for Wrapping<i16>

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impl Sub<&Wrapping<i32>> for &Wrapping<i32>

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impl Sub<&Wrapping<i32>> for Wrapping<i32>

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impl Sub<&Wrapping<i64>> for &Wrapping<i64>

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impl Sub<&Wrapping<i64>> for Wrapping<i64>

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impl Sub<&Wrapping<i128>> for &Wrapping<i128>

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impl Sub<&Wrapping<i128>> for Wrapping<i128>

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impl Sub<&Wrapping<isize>> for &Wrapping<isize>

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impl Sub<&Wrapping<isize>> for Wrapping<isize>

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impl Sub<&Wrapping<u8>> for &Wrapping<u8>

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impl Sub<&Wrapping<u8>> for Wrapping<u8>

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impl Sub<&Wrapping<u16>> for &Wrapping<u16>

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impl Sub<&Wrapping<u16>> for Wrapping<u16>

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impl Sub<&Wrapping<u32>> for &Wrapping<u32>

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impl Sub<&Wrapping<u32>> for Wrapping<u32>

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impl Sub<&Wrapping<u64>> for &Wrapping<u64>

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impl Sub<&Wrapping<u64>> for Wrapping<u64>

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impl Sub<&Wrapping<u128>> for &Wrapping<u128>

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impl Sub<&Wrapping<u128>> for Wrapping<u128>

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impl Sub<&Wrapping<usize>> for &Wrapping<usize>

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impl Sub<&Wrapping<usize>> for Wrapping<usize>

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impl Sub<&BigInt> for &i8

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impl Sub<&BigInt> for &i16

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impl Sub<&BigInt> for &i32

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impl Sub<&BigInt> for &i64

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impl Sub<&BigInt> for &i128

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impl Sub<&BigInt> for &isize

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impl Sub<&BigInt> for &u8

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impl Sub<&BigInt> for &u16

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impl Sub<&BigInt> for &u32

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impl Sub<&BigInt> for &u64

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impl Sub<&BigInt> for &u128

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impl Sub<&BigInt> for &usize

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impl Sub<&BigInt> for &BigInt

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impl Sub<&BigInt> for i8

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impl Sub<&BigInt> for i16

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impl Sub<&BigInt> for i32

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impl Sub<&BigInt> for i64

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impl Sub<&BigInt> for i128

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impl Sub<&BigInt> for isize

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impl Sub<&BigInt> for u8

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impl Sub<&BigInt> for u16

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impl Sub<&BigInt> for u32

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impl Sub<&BigInt> for u64

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impl Sub<&BigInt> for u128

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impl Sub<&BigInt> for usize

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impl Sub<&BigInt> for BigInt

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impl Sub<&BigUint> for &u8

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impl Sub<&BigUint> for &u16

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impl Sub<&BigUint> for &u32

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impl Sub<&BigUint> for &u64

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impl Sub<&BigUint> for &u128

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impl Sub<&BigUint> for &usize

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impl Sub<&BigUint> for &BigUint

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impl Sub<&BigUint> for u8

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impl Sub<&BigUint> for u16

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impl Sub<&BigUint> for u32

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impl Sub<&BigUint> for u64

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impl Sub<&BigUint> for u128

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impl Sub<&BigUint> for usize

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impl Sub<&BigUint> for BigUint

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impl Sub<i8> for &BigInt

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impl Sub<i8> for BigInt

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impl Sub<i16> for &BigInt

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impl Sub<i16> for BigInt

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impl Sub<i32> for &BigInt

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impl Sub<i32> for BigInt

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impl Sub<i64> for &BigInt

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impl Sub<i64> for BigInt

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impl Sub<i128> for &BigInt

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impl Sub<i128> for BigInt

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impl Sub<isize> for &BigInt

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impl Sub<isize> for BigInt

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impl Sub<u8> for &BigInt

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impl Sub<u8> for &BigUint

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impl Sub<u8> for BigInt

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impl Sub<u8> for BigUint

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impl Sub<u16> for &BigInt

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impl Sub<u16> for &BigUint

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impl Sub<u16> for BigInt

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impl Sub<u16> for BigUint

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impl Sub<u32> for &BigInt

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impl Sub<u32> for &BigUint

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impl Sub<u32> for BigInt

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impl Sub<u32> for BigUint

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impl Sub<u64> for &BigInt

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impl Sub<u64> for &BigUint

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impl Sub<u64> for BigInt

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impl Sub<u64> for BigUint

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impl Sub<u128> for &BigInt

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impl Sub<u128> for &BigUint

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impl Sub<u128> for BigInt

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impl Sub<u128> for BigUint

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impl Sub<usize> for &BigInt

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impl Sub<usize> for &BigUint

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impl Sub<usize> for BigInt

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impl Sub<usize> for BigUint

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impl Sub<Duration> for Instant

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impl Sub<Duration> for SystemTime

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impl Sub<BigInt> for &i8

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impl Sub<BigInt> for &i16

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impl Sub<BigInt> for &i32

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impl Sub<BigInt> for &i64

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impl Sub<BigInt> for &i128

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impl Sub<BigInt> for &isize

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impl Sub<BigInt> for &u8

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impl Sub<BigInt> for &u16

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impl Sub<BigInt> for &u32

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impl Sub<BigInt> for &u64

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impl Sub<BigInt> for &u128

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impl Sub<BigInt> for &usize

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impl Sub<BigInt> for &BigInt

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impl Sub<BigInt> for i8

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impl Sub<BigInt> for i16

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impl Sub<BigInt> for i32

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impl Sub<BigInt> for i64

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impl Sub<BigInt> for i128

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impl Sub<BigInt> for isize

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impl Sub<BigInt> for u8

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impl Sub<BigInt> for u16

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impl Sub<BigInt> for u32

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impl Sub<BigInt> for u64

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impl Sub<BigInt> for u128

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impl Sub<BigInt> for usize

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impl Sub<BigUint> for &u8

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impl Sub<BigUint> for &u16

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impl Sub<BigUint> for &u32

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impl Sub<BigUint> for &u64

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impl Sub<BigUint> for &u128

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impl Sub<BigUint> for &usize

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impl Sub<BigUint> for &BigUint

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impl Sub<BigUint> for u8

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impl Sub<BigUint> for u16

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impl Sub<BigUint> for u32

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impl Sub<BigUint> for u64

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impl Sub<BigUint> for u128

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impl Sub<BigUint> for usize

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impl Sub<B0> for UTerm

UTerm - B0 = Term

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impl Sub<B1> for UInt<UTerm, B1>

UInt<UTerm, B1> - B1 = UTerm

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impl<'a> Sub<f16> for &'a f16

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impl<'a> Sub<f32> for &'a f32

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impl<'a> Sub<f64> for &'a f64

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impl<'a> Sub<f128> for &'a f128

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impl<'a> Sub<i8> for &'a i8

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impl<'a> Sub<i16> for &'a i16

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impl<'a> Sub<i32> for &'a i32

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impl<'a> Sub<i64> for &'a i64

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impl<'a> Sub<i128> for &'a i128

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impl<'a> Sub<isize> for &'a isize

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impl<'a> Sub<u8> for &'a u8

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impl<'a> Sub<u16> for &'a u16

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impl<'a> Sub<u32> for &'a u32

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impl<'a> Sub<u64> for &'a u64

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impl<'a> Sub<u128> for &'a u128

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impl<'a> Sub<usize> for &'a usize

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impl<'a> Sub<Saturating<i8>> for &'a Saturating<i8>

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impl<'a> Sub<Saturating<i16>> for &'a Saturating<i16>

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impl<'a> Sub<Saturating<i32>> for &'a Saturating<i32>

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impl<'a> Sub<Saturating<i64>> for &'a Saturating<i64>

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impl<'a> Sub<Saturating<i128>> for &'a Saturating<i128>

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impl<'a> Sub<Saturating<isize>> for &'a Saturating<isize>

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impl<'a> Sub<Saturating<u8>> for &'a Saturating<u8>

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impl<'a> Sub<Saturating<u16>> for &'a Saturating<u16>

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impl<'a> Sub<Saturating<u32>> for &'a Saturating<u32>

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impl<'a> Sub<Saturating<u64>> for &'a Saturating<u64>

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impl<'a> Sub<Saturating<u128>> for &'a Saturating<u128>

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impl<'a> Sub<Saturating<usize>> for &'a Saturating<usize>

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impl<'a> Sub<Wrapping<i8>> for &'a Wrapping<i8>

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impl<'a> Sub<Wrapping<i16>> for &'a Wrapping<i16>

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impl<'a> Sub<Wrapping<i32>> for &'a Wrapping<i32>

1.14.0 · Source§

impl<'a> Sub<Wrapping<i64>> for &'a Wrapping<i64>

1.14.0 · Source§

impl<'a> Sub<Wrapping<i128>> for &'a Wrapping<i128>

1.14.0 · Source§

impl<'a> Sub<Wrapping<isize>> for &'a Wrapping<isize>

1.14.0 · Source§

impl<'a> Sub<Wrapping<u8>> for &'a Wrapping<u8>

1.14.0 · Source§

impl<'a> Sub<Wrapping<u16>> for &'a Wrapping<u16>

1.14.0 · Source§

impl<'a> Sub<Wrapping<u32>> for &'a Wrapping<u32>

1.14.0 · Source§

impl<'a> Sub<Wrapping<u64>> for &'a Wrapping<u64>

1.14.0 · Source§

impl<'a> Sub<Wrapping<u128>> for &'a Wrapping<u128>

1.14.0 · Source§

impl<'a> Sub<Wrapping<usize>> for &'a Wrapping<usize>

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impl<'a, F> Sub<&'a Evaluations<F>> for &Evaluations<F>
where F: PrimeField,

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impl<'a, F> Sub<&'a DensePolynomial<F>> for &DensePolynomial<F>
where F: Field,

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impl<'a, F> Sub<&'a SparsePolynomial<F>> for DensePolynomial<F>
where F: Field,

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impl<'a, F> Sub<&'a LinearCombination<F>> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<'a, F> Sub<(F, &'a LinearCombination<F>)> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<'a, P> Sub<&'a Projective<P>> for snarkvm_curves::templates::short_weierstrass_jacobian::projective::Projective<P>

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impl<'a, P> Sub<&'a Projective<P>> for snarkvm_curves::templates::twisted_edwards_extended::projective::Projective<P>

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impl<'a, P> Sub<&'a mut Projective<P>> for snarkvm_curves::templates::short_weierstrass_jacobian::projective::Projective<P>

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impl<'a, P> Sub<&'a mut Projective<P>> for snarkvm_curves::templates::twisted_edwards_extended::projective::Projective<P>

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impl<'a, P> Sub<&'a mut Fp6<P>> for Fp6<P>
where P: Fp6Parameters,

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impl<'a, P> Sub<&'a mut Fp2<P>> for Fp2<P>
where P: Fp2Parameters,

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impl<'a, P> Sub<&'a mut Fp12<P>> for Fp12<P>
where P: Fp12Parameters,

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impl<'a, P> Sub<&'a mut Fp256<P>> for Fp256<P>
where P: Fp256Parameters,

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impl<'a, P> Sub<&'a mut Fp384<P>> for Fp384<P>
where P: Fp384Parameters,

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impl<'lhs, 'rhs, T, const N: usize> Sub<&'rhs Simd<T, N>> for &'lhs Simd<T, N>
where T: SimdElement, Simd<T, N>: Sub<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

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type Output = Simd<T, N>

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impl<E> Sub for snarkvm_circuit::modules::Field<E>
where E: Environment,

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impl<E> Sub for snarkvm_circuit::modules::Group<E>
where E: Environment,

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impl<E> Sub for snarkvm_console_types_field::Field<E>
where E: Environment,

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impl<E> Sub for snarkvm_console_types_group::Group<E>
where E: Environment,

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impl<E> Sub for Scalar<E>
where E: Environment,

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impl<E> Sub<&Field<E>> for &snarkvm_circuit::modules::Field<E>
where E: Environment,

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impl<E> Sub<&Field<E>> for snarkvm_circuit::modules::Field<E>
where E: Environment,

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impl<E> Sub<&Group<E>> for &snarkvm_circuit::modules::Group<E>
where E: Environment,

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impl<E> Sub<&Group<E>> for snarkvm_circuit::modules::Group<E>
where E: Environment,

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impl<E> Sub<&Field<E>> for snarkvm_console_types_field::Field<E>
where E: Environment,

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impl<E> Sub<&Group<E>> for snarkvm_console_types_group::Group<E>
where E: Environment,

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impl<E> Sub<&Scalar<E>> for Scalar<E>
where E: Environment,

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impl<E> Sub<Field<E>> for &snarkvm_circuit::modules::Field<E>
where E: Environment,

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impl<E, I> Sub for snarkvm_circuit::modules::modules::integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Sub for snarkvm_console_types_integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Sub<&Integer<E, I>> for &snarkvm_circuit::modules::modules::integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Sub<&Integer<E, I>> for snarkvm_circuit::modules::modules::integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Sub<&Integer<E, I>> for snarkvm_console_types_integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<E, I> Sub<Integer<E, I>> for &snarkvm_circuit::modules::modules::integers::Integer<E, I>
where E: Environment, I: IntegerType,

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type Output = Integer<E, I>

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impl<F> Sub for Variable<F>
where F: PrimeField,

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impl<F> Sub for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Sub for snarkvm_circuit::prelude::LinearCombination<F>
where F: PrimeField,

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impl<F> Sub<&Variable<F>> for &Variable<F>
where F: PrimeField,

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impl<F> Sub<&Variable<F>> for Variable<F>
where F: PrimeField,

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impl<F> Sub<&Variable<F>> for snarkvm_circuit::prelude::LinearCombination<F>
where F: PrimeField,

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impl<F> Sub<&LinearCombination<F>> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Sub<&LinearCombination<F>> for &Variable<F>
where F: PrimeField,

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impl<F> Sub<&LinearCombination<F>> for &snarkvm_circuit::prelude::LinearCombination<F>
where F: PrimeField,

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impl<F> Sub<&LinearCombination<F>> for Variable<F>
where F: PrimeField,

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impl<F> Sub<&LinearCombination<F>> for snarkvm_circuit::prelude::LinearCombination<F>
where F: PrimeField,

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impl<F> Sub<(F, &LinearCombination<F>)> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Sub<(F, LinearCombination<F>)> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Sub<(F, LinearCombination<F>)> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Sub<(F, Variable)> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Sub<Variable<F>> for &Variable<F>
where F: PrimeField,

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impl<F> Sub<Variable<F>> for &snarkvm_circuit::prelude::LinearCombination<F>
where F: PrimeField,

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impl<F> Sub<Variable<F>> for snarkvm_circuit::prelude::LinearCombination<F>
where F: PrimeField,

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impl<F> Sub<LinearCombination<F>> for &snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Sub<Variable> for snarkvm_algorithms::r1cs::linear_combination::LinearCombination<F>
where F: Field,

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impl<F> Sub<LinearCombination<F>> for &Variable<F>
where F: PrimeField,

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impl<F> Sub<LinearCombination<F>> for &snarkvm_circuit::prelude::LinearCombination<F>
where F: PrimeField,

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impl<F> Sub<LinearCombination<F>> for Variable<F>
where F: PrimeField,

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impl<O> Sub for F32<O>
where O: ByteOrder,

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impl<O> Sub for F64<O>
where O: ByteOrder,

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impl<O> Sub for I16<O>
where O: ByteOrder,

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impl<O> Sub for I32<O>
where O: ByteOrder,

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impl<O> Sub for I64<O>
where O: ByteOrder,

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impl<O> Sub for I128<O>
where O: ByteOrder,

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impl<O> Sub for Isize<O>
where O: ByteOrder,

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impl<O> Sub for U16<O>
where O: ByteOrder,

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impl<O> Sub for U32<O>
where O: ByteOrder,

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impl<O> Sub for U64<O>
where O: ByteOrder,

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impl<O> Sub for U128<O>
where O: ByteOrder,

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impl<O> Sub for Usize<O>
where O: ByteOrder,

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impl<O> Sub<f32> for F32<O>
where O: ByteOrder,

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impl<O> Sub<f64> for F64<O>
where O: ByteOrder,

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impl<O> Sub<i16> for I16<O>
where O: ByteOrder,

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impl<O> Sub<i32> for I32<O>
where O: ByteOrder,

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impl<O> Sub<i64> for I64<O>
where O: ByteOrder,

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impl<O> Sub<i128> for I128<O>
where O: ByteOrder,

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impl<O> Sub<isize> for Isize<O>
where O: ByteOrder,

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impl<O> Sub<u16> for U16<O>
where O: ByteOrder,

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impl<O> Sub<u32> for U32<O>
where O: ByteOrder,

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impl<O> Sub<u64> for U64<O>
where O: ByteOrder,

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impl<O> Sub<u128> for U128<O>
where O: ByteOrder,

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impl<O> Sub<usize> for Usize<O>
where O: ByteOrder,

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impl<O> Sub<F32<O>> for f32
where O: ByteOrder,

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impl<O> Sub<F64<O>> for f64
where O: ByteOrder,

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impl<O> Sub<I16<O>> for i16
where O: ByteOrder,

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impl<O> Sub<I32<O>> for i32
where O: ByteOrder,

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impl<O> Sub<I64<O>> for i64
where O: ByteOrder,

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impl<O> Sub<I128<O>> for i128
where O: ByteOrder,

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impl<O> Sub<Isize<O>> for isize
where O: ByteOrder,

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impl<O> Sub<U16<O>> for u16
where O: ByteOrder,

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impl<O> Sub<U32<O>> for u32
where O: ByteOrder,

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impl<O> Sub<U64<O>> for u64
where O: ByteOrder,

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impl<O> Sub<U128<O>> for u128
where O: ByteOrder,

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impl<O> Sub<Usize<O>> for usize
where O: ByteOrder,

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impl<P> Sub for snarkvm_curves::templates::short_weierstrass_jacobian::projective::Projective<P>

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impl<P> Sub for snarkvm_curves::templates::twisted_edwards_extended::projective::Projective<P>

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impl<P> Sub for Fp6<P>
where P: Fp6Parameters,

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impl<P> Sub for Fp2<P>
where P: Fp2Parameters,

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impl<P> Sub for Fp12<P>
where P: Fp12Parameters,

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impl<P> Sub for Fp256<P>
where P: Fp256Parameters,

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impl<P> Sub for Fp384<P>
where P: Fp384Parameters,

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impl<P> Sub<&&Projective<P>> for snarkvm_curves::templates::short_weierstrass_jacobian::projective::Projective<P>

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impl<P> Sub<&&Projective<P>> for snarkvm_curves::templates::twisted_edwards_extended::projective::Projective<P>

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impl<P> Sub<&&Fp6<P>> for Fp6<P>
where P: Fp6Parameters,

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impl<P> Sub<&&Fp2<P>> for Fp2<P>
where P: Fp2Parameters,

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impl<P> Sub<&&Fp12<P>> for Fp12<P>
where P: Fp12Parameters,

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impl<P> Sub<&&Fp256<P>> for Fp256<P>
where P: Fp256Parameters,

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impl<P> Sub<&&Fp384<P>> for Fp384<P>
where P: Fp384Parameters,

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impl<P> Sub<&Fp6<P>> for Fp6<P>
where P: Fp6Parameters,

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impl<P> Sub<&Fp2<P>> for Fp2<P>
where P: Fp2Parameters,

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impl<P> Sub<&Fp12<P>> for Fp12<P>
where P: Fp12Parameters,

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impl<P> Sub<&Fp256<P>> for Fp256<P>
where P: Fp256Parameters,

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impl<P> Sub<&Fp384<P>> for Fp384<P>
where P: Fp384Parameters,

1.0.0 · Source§

impl<T, A> Sub<&BTreeSet<T, A>> for &BTreeSet<T, A>
where T: Ord + Clone, A: Allocator + Clone,

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impl<T, S1, S2> Sub<&IndexSet<T, S2>> for &IndexSet<T, S1>
where T: Eq + Hash + Clone, S1: BuildHasher + Default, S2: BuildHasher,

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type Output = IndexSet<T, S1>

1.0.0 · Source§

impl<T, S> Sub<&HashSet<T, S>> for &std::collections::hash::set::HashSet<T, S>
where T: Eq + Hash + Clone, S: BuildHasher + Default,

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type Output = HashSet<T, S>

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impl<T, S> Sub<&HashSet<T, S>> for &hashbrown::set::HashSet<T, S>
where T: Eq + Hash + Clone, S: BuildHasher + Default,

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type Output = HashSet<T, S>

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impl<T, S, A> Sub<&HashSet<T, S, A>> for &hashbrown::set::HashSet<T, S, A>
where T: Eq + Hash + Clone, S: BuildHasher + Default, A: Allocator + Default,

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type Output = HashSet<T, S, A>

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impl<T, const N: usize> Sub<&Simd<T, N>> for Simd<T, N>
where T: SimdElement, Simd<T, N>: Sub<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

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type Output = Simd<T, N>

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impl<T, const N: usize> Sub<Simd<T, N>> for &Simd<T, N>
where T: SimdElement, Simd<T, N>: Sub<Output = Simd<T, N>>, LaneCount<N>: SupportedLaneCount,

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type Output = Simd<T, N>

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impl<U> Sub<B1> for UInt<U, B0>
where U: Unsigned + Sub<B1>, <U as Sub<B1>>::Output: Unsigned,

UInt<U, B0> - B1 = UInt<U - B1, B1>

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type Output = UInt<<U as Sub<B1>>::Output, B1>

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impl<U> Sub<NInt<U>> for Z0
where U: Unsigned + NonZero,

Z0 - N = P

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impl<U> Sub<PInt<U>> for Z0
where U: Unsigned + NonZero,

Z0 - P = N

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impl<U> Sub<Z0> for NInt<U>
where U: Unsigned + NonZero,

NInt - Z0 = NInt

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impl<U> Sub<Z0> for PInt<U>
where U: Unsigned + NonZero,

PInt - Z0 = PInt

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impl<U, B> Sub<B0> for UInt<U, B>
where U: Unsigned, B: Bit,

UInt - B0 = UInt

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type Output = UInt<U, B>

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impl<U, B> Sub<B1> for UInt<UInt<U, B>, B1>
where U: Unsigned, B: Bit,

UInt<U, B1> - B1 = UInt<U, B0>

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type Output = UInt<UInt<U, B>, B0>

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impl<Ul, Bl, Ur> Sub<Ur> for UInt<Ul, Bl>
where Ul: Unsigned, Bl: Bit, Ur: Unsigned, UInt<Ul, Bl>: PrivateSub<Ur>, <UInt<Ul, Bl> as PrivateSub<Ur>>::Output: Trim,

Subtracting unsigned integers. We just do our PrivateSub and then Trim the output.

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type Output = <<UInt<Ul, Bl> as PrivateSub<Ur>>::Output as Trim>::Output

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impl<Ul, Ur> Sub<NInt<Ur>> for NInt<Ul>
where Ul: Unsigned + NonZero, Ur: Unsigned + NonZero + Cmp<Ul> + PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>,

N(Ul) - N(Ur): We resolve this with our PrivateAdd

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type Output = <Ur as PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>>::Output

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impl<Ul, Ur> Sub<NInt<Ur>> for PInt<Ul>
where Ul: Unsigned + NonZero + Add<Ur>, Ur: Unsigned + NonZero, <Ul as Add<Ur>>::Output: Unsigned + NonZero,

P(Ul) - N(Ur) = P(Ul + Ur)

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type Output = PInt<<Ul as Add<Ur>>::Output>

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impl<Ul, Ur> Sub<PInt<Ur>> for NInt<Ul>
where Ul: Unsigned + NonZero + Add<Ur>, Ur: Unsigned + NonZero, <Ul as Add<Ur>>::Output: Unsigned + NonZero,

N(Ul) - P(Ur) = N(Ul + Ur)

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type Output = NInt<<Ul as Add<Ur>>::Output>

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impl<Ul, Ur> Sub<PInt<Ur>> for PInt<Ul>
where Ul: Unsigned + NonZero + Cmp<Ur> + PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>, Ur: Unsigned + NonZero,

P(Ul) - P(Ur): We resolve this with our PrivateAdd

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type Output = <Ul as PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>>::Output

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impl<Vl, Al, Vr, Ar> Sub<TArr<Vr, Ar>> for TArr<Vl, Al>
where Vl: Sub<Vr>, Al: Sub<Ar>,

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type Output = TArr<<Vl as Sub<Vr>>::Output, <Al as Sub<Ar>>::Output>

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impl<const N: usize> Sub for Simd<f32, N>

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impl<const N: usize> Sub for Simd<f64, N>

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impl<const N: usize> Sub for Simd<i8, N>

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impl<const N: usize> Sub for Simd<i16, N>

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impl<const N: usize> Sub for Simd<i32, N>

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impl<const N: usize> Sub for Simd<i64, N>

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impl<const N: usize> Sub for Simd<isize, N>

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impl<const N: usize> Sub for Simd<u8, N>

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impl<const N: usize> Sub for Simd<u16, N>

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impl<const N: usize> Sub for Simd<u32, N>

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impl<const N: usize> Sub for Simd<u64, N>

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impl<const N: usize> Sub for Simd<usize, N>