def length_rev

bend-collections-laws-math@1.0.0.0 · proofs/lib/list.bend:215

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

215def length_rev(-A: Data, +xs: List<&2, A>) -> {SC.length(A, SC.reverse(A, xs)) == SC.length(A, xs) : Nat}:
216  match xs:
217    case Nil{}:
218      {==}
219    case Con{+h, +t}:
220      Equal.trans(Nat, SC.length(A, SC.snoc(A, SC.reverse(A, t), h)), 1n+SC.length(A, SC.reverse(A, t)), 1n+SC.length(A, t), length_snoc(A, SC.reverse(A, t), h), N.succ_cong(SC.length(A, SC.reverse(A, t)), SC.length(A, t), length_rev(A, t)))