def internal_length_reverse_go

bend-mathlib@0.8.1.0 · list.bend:122

import Base
import bend-mathlib@0.8.1.0/nat.bend as MNat

122def internal_length_reverse_go(a, -A: Kind(a), xs: List<a, A>, -acc: List<a, A>, +n: Nat, e: {List.length(a, A, acc) == n : Nat}) -> {List.length(a, A, List.reverse.go(a, A, xs, acc)) == Nat.add(n, List.length(a, A, xs)) : Nat}:
123  match xs:
124    case Nil{}:
125      %Equal.sym(Nat, Nat.add(n, 0n), n, MNat.add_zero(n)) : {List.length(a, A, acc) == _ : Nat}
126      e
127    case h <> t:
128      %Equal.sym(Nat, Nat.add(n, 1n+List.length(a, A, t)), 1n+Nat.add(n, List.length(a, A, t)), MNat.add_succ(n, List.length(a, A, t))) : {List.length(a, A, List.reverse.go(a, A, t, h <> acc)) == _ : Nat}
129      internal_length_reverse_go(a, A, t, h <> acc, 1n+n, Equal.cong(Nat, Nat, k => 1n+k, List.length(a, A, acc), n, e))