WordComparison.u32_refines: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/word_comparison.bend as WordComparison
Lines 44-49 of bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/word_comparison.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/word_comparison.bend&start_line=44&end_line=49

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 N

def u32_refines(a: U32, b: U32) -> {U32.cmp(a, b) == Nat.cmp(U32.to_nat(a), U32.to_nat(b)) : Cmp}:
  match a b:
    case U32{+x} U32{+y}:
      %Equal.sym(Nat, Word.to_nat(32n, x), S.unsigned(32n, x), N.primitive_word_interpretation(32n, x)) : {U32.cmp(U32{x}, U32{y}) == Nat.cmp(_, Word.to_nat(32n, y)) : Cmp}
      %Equal.sym(Nat, Word.to_nat(32n, y), S.unsigned(32n, y), N.primitive_word_interpretation(32n, y)) : {U32.cmp(U32{x}, U32{y}) == Nat.cmp(S.unsigned(32n, x), _) : Cmp}
      refines(32n, x, y)

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  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.cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.cmp
  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.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/word_comparison.bend&name=refines
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned