def length_append

bendtorch-core@0.1.0.0 · src/autograd/backward_PROOF.bend:39

import Base

39def length_append(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>) ->
40  {List.length(&2, A, List.append(&2, A, xs, ys)) == Nat.add(List.length(&2, A, xs), List.length(&2, A, ys)) : Nat}:
41  match xs:
42    case Nil{}:
43      {==}
44    case Con{head, tail}:
45      Equal.cong(Nat, Nat, number => 1n+number, List.length(&2, A, List.append(&2, A, tail, ys)),
46        Nat.add(List.length(&2, A, tail), List.length(&2, A, ys)), length_append(A, tail, ys))