List.internal_mem_append_left: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 739-745 of bend-mathlib@0.8.1.0/list.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/list.bend&start_line=739&end_line=745

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

def 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}:
  match xs:
    case Nil{}:
      Empty.absurd({List.contains(~Nat, ~Nat.is_eq, ys, x) == True{} : Bool}, MNat.internal_false_ne_true(h))
    case hd <> tl:
      %internal_contains_cons(~Nat, ~Nat.is_eq, hd, List.append(&2, Nat, tl, ys), x) : {_ == True{} : Bool}
      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))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.contains
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=internal_contains_cons
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=internal_or_of_or
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/nat.bend&name=internal_false_ne_true