W64div.mstep: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64div.bend as W64div
Lines 86-89 of bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64div.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/typed/w64div.bend&start_line=86&end_line=89

import Base
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as NR

def mstep(+dp: Nat, +x: Nat, +b: Nat, +g: Nat) -> {Nat.mod(Nat.add(Nat.mul(Nat.mod(x, 1n+dp), b), g), 1n+dp) == Nat.mod(Nat.add(Nat.mul(x, b), g), 1n+dp) : Nat}:
  +y = Nat.mul(Nat.mod(x, 1n+dp), b)
  Equal.trans(Nat, Nat.mod(Nat.add(y, g), 1n+dp), Nat.mod(Nat.add(Nat.mod(y, 1n+dp), g), 1n+dp), Nat.mod(Nat.add(Nat.mul(x, b), g), 1n+dp), Equal.sym(Nat, Nat.mod(Nat.add(Nat.mod(y, 1n+dp), g), 1n+dp), Nat.mod(Nat.add(y, g), 1n+dp), NR.mod_add_l(dp, y, g)),
    Equal.trans(Nat, Nat.mod(Nat.add(Nat.mod(y, 1n+dp), g), 1n+dp), Nat.mod(Nat.add(Nat.mod(Nat.mul(x, b), 1n+dp), g), 1n+dp), Nat.mod(Nat.add(Nat.mul(x, b), g), 1n+dp), Equal.cong(Nat, Nat, t => Nat.mod(Nat.add(t, g), 1n+dp), Nat.mod(y, 1n+dp), Nat.mod(Nat.mul(x, b), 1n+dp), NR.mod_mul_l(dp, x, b)), NR.mod_add_l(dp, Nat.mul(x, b), g)))

Uses (9):
  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.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=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=mod_add_l
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend&name=mod_mul_l