def rev_append

bend-collections-laws-math@1.0.0.0 · proofs/lib/list.bend:206

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

206def rev_append(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>) -> {SC.reverse(A, SC.append(A, xs, ys)) == SC.append(A, SC.reverse(A, ys), SC.reverse(A, xs)) : List<&2, A>}:
207  match xs:
208    case Nil{}:
209      Equal.sym(List<&2, A>, SC.append(A, SC.reverse(A, ys), Nil{}), SC.reverse(A, ys), append_nil(A, SC.reverse(A, ys)))
210    case Con{+h, +t}:
211      Equal.trans(List<&2, A>, SC.snoc(A, SC.reverse(A, SC.append(A, t, ys)), h), SC.snoc(A, SC.append(A, SC.reverse(A, ys), SC.reverse(A, t)), h), SC.append(A, SC.reverse(A, ys), SC.snoc(A, SC.reverse(A, t), h)),
212        Equal.cong(List<&2, A>, List<&2, A>, zs => SC.snoc(A, zs, h), SC.reverse(A, SC.append(A, t, ys)), SC.append(A, SC.reverse(A, ys), SC.reverse(A, t)), rev_append(A, t, ys)),
213        Equal.sym(List<&2, A>, SC.append(A, SC.reverse(A, ys), SC.snoc(A, SC.reverse(A, t), h)), SC.snoc(A, SC.append(A, SC.reverse(A, ys), SC.reverse(A, t)), h), append_snoc(A, SC.reverse(A, ys), SC.reverse(A, t), h)))