U32alg.w_zero_add: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend as U32alg
Lines 108-114 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&start_line=108&end_line=114

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend as U

def w_zero_add(+n: Nat, +b: Word(n)) -> {Word.add(n, Word.zero(n), b) == b : Word(n)}:
  +e = cons(n, Word.zero(n), b)
  +e2 = Equal.trans(Nat, Nat.add(uw(n, Word.add(n, Word.zero(n), b)), sc(n, cy(n, Word.zero(n), b, False{}))), Nat.add(uw(n, Word.zero(n)), uw(n, b)), Nat.add(uw(n, b), sc(n, 0n)), e,
    %Equal.sym(Nat, uw(n, Word.zero(n)), 0n, uw_zero(n)) : {Nat.add(_, uw(n, b)) == Nat.add(uw(n, b), sc(n, 0n)) : Nat}
    %Equal.sym(Nat, sc(n, 0n), 0n, sc_zero(n)) : {uw(n, b) == Nat.add(uw(n, b), _) : Nat}
    Equal.sym(Nat, Nat.add(uw(n, b), 0n), uw(n, b), N.add_zero(uw(n, b))))
  w_inj(n, Word.add(n, Word.zero(n), b), b, uniq(n, uw(n, Word.add(n, Word.zero(n), b)), uw(n, b), cy(n, Word.zero(n), b, False{}), 0n, e2, U.WB_unsigned(n, Word.add(n, Word.zero(n), b)), U.WB_unsigned(n, b)))

Uses (18):
  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=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=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32.bend&name=WB_unsigned
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=cons
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=cy
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=sc_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=uniq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=uw
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=uw_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/u32alg.bend&name=w_inj