def unscale

bend-collections-laws-math@1.0.0.0 · proofs/math/natural/lcm.bend:65

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as A
import bend-collections-laws-math@1.0.0.0/proofs/math/natural/arith.bend as R

65# c x == w (h c) gives x == w h (c > 0)
66def unscale(+cp: Nat, +x: Nat, +w: Nat, +h: Nat, +e: {Nat.mul(1n+cp, x) == Nat.mul(w, Nat.mul(h, 1n+cp)) : Nat}) -> {x == Nat.mul(w, h) : Nat}:
67  R.mul_cancel(x, Nat.mul(w, h), cp, Equal.trans(Nat, Nat.mul(x, 1n+cp), Nat.mul(1n+cp, x), Nat.mul(Nat.mul(w, h), 1n+cp), A.mul_comm(x, 1n+cp), Equal.trans(Nat, Nat.mul(1n+cp, x), Nat.mul(w, Nat.mul(h, 1n+cp)), Nat.mul(Nat.mul(w, h), 1n+cp), e, Equal.sym(Nat, Nat.mul(Nat.mul(w, h), 1n+cp), Nat.mul(w, Nat.mul(h, 1n+cp)), A.mul_assoc(w, h, 1n+cp)))))