GradientPROOF.word_exact: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend as GradientPROOF
Lines 106-111 of bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&start_line=106&end_line=111

import Base
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle
import bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend as Conversion

def word_exact(+left: U32, +right: U32, equal: {True{} == Nat.is_eq(U32.to_nat(left), U32.to_nat(right)) : Bool}) -> Holds<{left == right : U32}>:
  Holds{
    %Conversion.word_natural_exact(left) : {_ == right : U32}
    %Conversion.word_natural_exact(right) : {U32.from_nat(U32.to_nat(left)) == _ : U32}
    Equal.cong(Nat, U32, U32.from_nat, U32.to_nat(left), U32.to_nat(right),
      Lifecycle.natural_equal(U32.to_nat(left), U32.to_nat(right), equal))}

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&name=Holds
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend&name=natural_equal
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend&name=word_natural_exact