U32.inc_from: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend as U32
Lines 73-78 of bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/u32.bend&start_line=73&end_line=78

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/modular_addition.bend as MA

# one increment over an abstract width (the checker never expands a
# literal-width word here)
def inc_from(+n: Nat, +p: Nat, +hv: {S.unsigned(n, S.from_nat(n, p)) == p : Nat}) -> {Word.inc(n, S.from_nat(n, p)) == S.from_nat(n, 1n+p) : Word(n)}:
  Equal.trans(Word(n), Word.inc(n, S.from_nat(n, p)), S.from_nat(n, 1n+S.unsigned(n, S.from_nat(n, p))), S.from_nat(n, 1n+p),
    MA.increment_refines(n, S.from_nat(n, p)),
    Equal.cong(Nat, Word(n), v => S.from_nat(n, 1n+v), S.unsigned(n, S.from_nat(n, p)), p, hv))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.inc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/modular_addition.bend&name=increment_refines
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=from_nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=unsigned