def plus1

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/natfuel.bend:469

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

469def plus1(+x: Nat) -> {Nat.add(x, 1n) == 1n+x : Nat}:
470  Equal.trans(Nat, Nat.add(x, 1n), 1n+Nat.add(x, 0n), 1n+x, NA.add_succ(x, 0n), Equal.cong(Nat, Nat, t => 1n+t, Nat.add(x, 0n), x, N.add_zero(x)))