Arith.mul_sc1: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend as Arith
Lines 23-24 of bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend&start_line=23&end_line=24

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

def mul_sc1(+k: Nat, +one: Nat, +h1: {one == 1n : Nat}, +x: Nat) -> {Nat.mul(x, sc(k, one)) == sc(k, x) : Nat}:
  L.subst(Nat, o => {Nat.mul(x, S.scale_binary(k, o)) == S.scale_binary(k, x) : Nat}, 1n, one, Equal.sym(Nat, one, 1n, h1), mul_sc(k, x))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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-math@1.0.0.0/proofs/lib/arith.bend&name=mul_sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend&name=sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend&name=scale_binary
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=subst