def swap_cw

bend-collections-laws-crypto@1.0.0.0 · proofs/math/natural/lcm.bend:53

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A

53# c (w g) == w (c g)
54def swap_cw(+c: Nat, +w: Nat, +g: Nat) -> {Nat.mul(c, Nat.mul(w, g)) == Nat.mul(w, Nat.mul(c, g)) : Nat}:
55  Equal.trans(Nat, Nat.mul(c, Nat.mul(w, g)), Nat.mul(Nat.mul(c, w), g), Nat.mul(w, Nat.mul(c, g)),
56    Equal.sym(Nat, Nat.mul(Nat.mul(c, w), g), Nat.mul(c, Nat.mul(w, g)), A.mul_assoc(c, w, g)),
57    Equal.trans(Nat, Nat.mul(Nat.mul(c, w), g), Nat.mul(Nat.mul(w, c), g), Nat.mul(w, Nat.mul(c, g)),
58      Equal.cong(Nat, Nat, z => Nat.mul(z, g), Nat.mul(c, w), Nat.mul(w, c), A.mul_comm(c, w)),
59      A.mul_assoc(w, c, g)))