PROOF.h.eq_sym_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 2361-2373 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=2361&end_line=2373

import Base

# eq is symmetric on False, given refl and sound.
def h.eq_sym_f.c(
  ~K: Data, ~eq: K -> K -> Bool, ~refl: @x: K -> {eq(x, x) == True{} : Bool},
  ~sound: @x: K -> @y: K -> {eq(x, y) == True{} : Bool} -> {x == y : K},
  +k: K, +key: K, e: {eq(k, key) == False{} : Bool}, b: Bool, eb: {b == eq(key, k) : Bool}
) -> {b == False{} : Bool}:
  match b:
    case True{}:
      h.tf({True{} == False{} : Bool}, eq(k, k), refl(k),
        rw(K, z => {eq(k, z) == False{} : Bool}, k, key,
          Equal.sym(K, key, k, sound(key, k, h.sb(True{}, eq(key, k), eb))), e))
    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=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.sb
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=h.tf
  https://jend.leeeet.dev/definition.txt?path=bend-kit-collections@0.1.4.1/PROOF.bend&name=rw