Lcm.swap_cw: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend as Lcm
Lines 53-59 of bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/natural/lcm.bend&start_line=53&end_line=59

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

# c (w g) == w (c g)
def swap_cw(+c: Nat, +w: Nat, +g: Nat) -> {Nat.mul(c, Nat.mul(w, g)) == Nat.mul(w, Nat.mul(c, g)) : Nat}:
  Equal.trans(Nat, Nat.mul(c, Nat.mul(w, g)), Nat.mul(Nat.mul(c, w), g), Nat.mul(w, Nat.mul(c, g)),
    Equal.sym(Nat, Nat.mul(Nat.mul(c, w), g), Nat.mul(c, Nat.mul(w, g)), A.mul_assoc(c, w, g)),
    Equal.trans(Nat, Nat.mul(Nat.mul(c, w), g), Nat.mul(Nat.mul(w, c), g), Nat.mul(w, Nat.mul(c, g)),
      Equal.cong(Nat, Nat, z => Nat.mul(z, g), Nat.mul(c, w), Nat.mul(w, c), A.mul_comm(c, w)),
      A.mul_assoc(w, c, g)))

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.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.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=mul_comm