Password.sub_cancel: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/password.bend as Password
Lines 90-92 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/password.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/password.bend&start_line=90&end_line=92

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/lemmas/proofs/nat_algebra.bend as NA

def sub_cancel(+c: Nat, +m: Nat, +r: Nat) -> {Nat.sub(Nat.add(c, Nat.add(m, r)), m) == Nat.add(c, r) : Nat}:
  %Equal.sym(Nat, Nat.add(c, Nat.add(m, r)), Nat.add(m, Nat.add(c, r)), NA.add_swap(c, m, r)) : {Nat.sub(_, m) == Nat.add(c, r) : Nat}
  N.add_sub_cancel(m, Nat.add(c, r))

Uses (6):
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=add_swap
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=add_sub_cancel