def rev_snoc

bend-collections-laws-math@1.0.0.0 · proofs/lib/list.bend:191

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

191def rev_snoc(-A: Data, +xs: List<&2, A>, +x: A) -> {SC.reverse(A, SC.snoc(A, xs, x)) == Con{x, SC.reverse(A, xs)} : List<&2, A>}:
192  match xs:
193    case Nil{}:
194      {==}
195    case Con{+h, +t}:
196      Equal.cong(List<&2, A>, List<&2, A>, zs => SC.snoc(A, zs, h), SC.reverse(A, SC.snoc(A, t, x)), Con{x, SC.reverse(A, t)}, rev_snoc(A, t, x))