def double_succ

bend-collections-laws-math@1.0.0.0 · proofs/lib/nat.bend:517

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

517def double_succ(+y: Nat) -> {Nat.double(1n+y) == Nat.add(2n, Nat.double(y)) : Nat}:
518  %Equal.sym(Nat, Nat.double(y), Nat.add(y, y), NA.double_self(y)) : {Nat.double(1n+y) == Nat.add(2n, _) : Nat}
519  %Equal.sym(Nat, Nat.double(1n+y), Nat.add(1n+y, 1n+y), NA.double_self(1n+y)) : {_ == Nat.add(2n, Nat.add(y, y)) : Nat}
520  succ_cong(Nat.add(y, 1n+y), 1n+Nat.add(y, y), add_succ(y, y))