PROOF.h.ne_f.c: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 2060-2070 of bend-kit-collections@0.1.4.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&start_line=2060&end_line=2070

import Base

# eq(k, k2) is False when k2 != k.
def h.ne_f.c(
  ~K: Data, ~eq: K -> K -> Bool,
  ~sound: @x: K -> @y: K -> {eq(x, y) == True{} : Bool} -> {x == y : K},
  +k2: K, +k: K, ne: {k2 != k : K}, b: Bool, eb: {b == eq(k, k2) : Bool}
) -> {b == False{} : Bool}:
  match b:
    case True{}:
      Empty.absurd({True{} == False{} : Bool}, ne(Equal.sym(K, k, k2, sound(k, k2, h.sb(True{}, eq(k, k2), eb)))))
    case False{}:
      {==}

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty
  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.sym
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.sb