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def un.double_mul

bend-osdev-u32@0.1.0.0 · PROOF.bend:979

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

979def un.double_mul(+x: Nat, +y: Nat) -> {Nat.mul(Nat.double(x), y) == Nat.double(Nat.mul(x, y)) : Nat}:
980  Equal.trans(Nat, Nat.mul(Nat.double(x), y), Nat.add(Nat.mul(x, y), Nat.mul(x, y)), Nat.double(Nat.mul(x, y)), Equal.trans(Nat, Nat.mul(Nat.double(x), y), Nat.mul(Nat.add(x, x), y), Nat.add(Nat.mul(x, y), Nat.mul(x, y)), Equal.cong(Nat, Nat, zz => Nat.mul(zz, y), Nat.double(x), Nat.add(x, x), Laws.nat_double(x)), Laws.nat_add_mul(x, x, y)), Equal.sym(Nat, Nat.double(Nat.mul(x, y)), Nat.add(Nat.mul(x, y), Nat.mul(x, y)), Laws.nat_double(Nat.mul(x, y))))

Uses (9)

Used by (1)