def sq_sc

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/w64mul.bend:54

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend as AR

54def sq_sc(+k: Nat, +one: Nat, +h1: {one == 1n : Nat}) -> {Nat.mul(WD.sc(k, one), WD.sc(k, one)) == WD.sc(Nat.add(k, k), one) : Nat}:
55  Equal.trans(Nat, Nat.mul(WD.sc(k, one), WD.sc(k, one)), WD.sc(k, WD.sc(k, one)), WD.sc(Nat.add(k, k), one), AR.mul_sc1(k, one, h1, WD.sc(k, one)), Equal.sym(Nat, WD.sc(Nat.add(k, k), one), WD.sc(k, WD.sc(k, one)), AR.sc_idx(k, k, one)))