def internal_mem_append_left

bend-mathlib@0.8.1.0 · list.bend:739

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

739def internal_mem_append_left(+xs: List<&2, Nat>, +ys: List<&2, Nat>, +x: Nat, h: {List.contains(~Nat, ~Nat.is_eq, xs, x) == True{} : Bool}) -> {List.contains(~Nat, ~Nat.is_eq, List.append(&2, Nat, xs, ys), x) == True{} : Bool}:
740  match xs:
741    case Nil{}:
742      Empty.absurd({List.contains(~Nat, ~Nat.is_eq, ys, x) == True{} : Bool}, MNat.internal_false_ne_true(h))
743    case hd <> tl:
744      %internal_contains_cons(~Nat, ~Nat.is_eq, hd, List.append(&2, Nat, tl, ys), x) : {_ == True{} : Bool}
745      internal_or_of_or(Nat.is_eq(hd, x), List.contains(~Nat, ~Nat.is_eq, tl, x), List.contains(~Nat, ~Nat.is_eq, List.append(&2, Nat, tl, ys), x), Equal.trans(Bool, Bool.or(Nat.is_eq(hd, x), List.contains(~Nat, ~Nat.is_eq, tl, x)), List.contains(~Nat, ~Nat.is_eq, hd <> tl, x), True{}, internal_contains_cons(~Nat, ~Nat.is_eq, hd, tl, x), h), internal_mem_append_left(tl, ys, x))