SubtractionBounds.u32_exact: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend as SubtractionBounds
Lines 52-58 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend&start_line=52&end_line=58

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/numeric.bend as Numeric

def u32_exact(a: U32, b: U32, enough: {Nat.is_le(U32.to_nat(b), U32.to_nat(a)) == True{} : Bool}) -> {U32.to_nat(U32.sub(a, b)) == Nat.sub(U32.to_nat(a), U32.to_nat(b)) : Nat}:
  match a b:
    case U32{+x} U32{+y}:
      %Equal.sym(Nat, Word.to_nat(32n, Word.sub(32n, x, y)), S.unsigned(32n, Word.sub(32n, x, y)), Numeric.primitive_word_interpretation(32n, Word.sub(32n, x, y))) : {_ == Nat.sub(Word.to_nat(32n, x), Word.to_nat(32n, y)) : Nat}
      %Equal.sym(Nat, Word.to_nat(32n, x), S.unsigned(32n, x), Numeric.primitive_word_interpretation(32n, x)) : {S.unsigned(32n, Word.sub(32n, x, y)) == Nat.sub(_, Word.to_nat(32n, y)) : Nat}
      %Equal.sym(Nat, Word.to_nat(32n, y), S.unsigned(32n, y), Numeric.primitive_word_interpretation(32n, y)) : {S.unsigned(32n, Word.sub(32n, x, y)) == Nat.sub(S.unsigned(32n, x), _) : Nat}
      exact(32n, x, y, primitive_bound(x, y, enough))

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/numeric.bend&name=primitive_word_interpretation
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend&name=exact
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/subtraction_bounds.bend&name=primitive_bound
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned