def internal_apply_length

bend-mathlib@0.8.1.0 · perm.bend:328

import Base
import bendlib-kernel-list@1.0.0.0/list.bend as K

328def internal_apply_length(-A: Data, +s: List<&2, Nat>, +xs: List<&2, A>) -> {List.length(&2, A, K.apply(A, s, xs)) == List.length(&2, A, xs) : Nat}:
329  match s:
330    case Nil{}:
331      {==}
332    case +i <> rest:
333      Equal.trans(Nat, List.length(&2, A, K.apply(A, rest, K.swap_at(A, i, xs))), List.length(&2, A, K.swap_at(A, i, xs)), List.length(&2, A, xs), internal_apply_length(A, rest, K.swap_at(A, i, xs)), internal_swap_at_length(A, i, xs))