PROOF.pk.go_skip: def of bend-osdev-pkcs7@0.1.0.0
Import: import bend-osdev-pkcs7@0.1.0.0/PROOF.bend as PROOF
Lines 130-136 of bend-osdev-pkcs7@0.1.0.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-pkcs7@0.1.0.0/PROOF.bend&start_line=130&end_line=136

import Base
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

# 1 + m + x steps from (m, d, r) take one wrap and leave x
def pk.go_skip(+m: Nat, +x: Nat, +d: Nat, +r: Nat) -> {Nat.divmod.go(1n+Nat.add(m, x), m, d, r) == Nat.divmod.go(x, Nat.add(m, r), 1n+d, 0n) : Nat & Nat}:
  match m:
    case 0n:
      {==}
    case 1n+mp:
      Equal.trans(Nat & Nat, Nat.divmod.go(1n+Nat.add(mp, x), mp, d, 1n+r), Nat.divmod.go(x, Nat.add(mp, 1n+r), 1n+d, 0n), Nat.divmod.go(x, 1n+Nat.add(mp, r), 1n+d, 0n), pk.go_skip(mp, x, d, 1n+r), Equal.cong(Nat, Nat & Nat, z => Nat.divmod.go(x, z, 1n+d, 0n), Nat.add(mp, 1n+r), 1n+Nat.add(mp, r), UL.nat_add_succ(mp, r)))

Uses (7):
  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=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.divmod.go
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_succ