PROOF.h.fin_hd: def of bend-kit-collections@0.1.4.1
Import: import bend-kit-collections@0.1.4.1/PROOF.bend as PROOF
Lines 1780-1796 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=1780&end_line=1796

import Base
import bend-mathlib@0.7.4.0/bool.bend as MBool

def h.fin_hd(t: Cmp, x: Bool, y: Bool, e: {Cmp.is_eq(Word.cmp.fin(x, y, t)) == True{} : Bool})
  -> {x == y : Bool}:
  match t:
    case LT{}:
      Empty.absurd({x == y : Bool}, MBool.false_ne_true()(e))
    case EQ{}:
      match x y:
        case False{} False{}:
          {==}
        case False{} True{}:
          Empty.absurd({False{} == True{} : Bool}, MBool.false_ne_true()(e))
        case True{} False{}:
          Empty.absurd({True{} == False{} : Bool}, MBool.false_ne_true()(e))
        case True{} True{}:
          {==}
    case GT{}:
      Empty.absurd({x == y : Bool}, MBool.false_ne_true()(e))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Cmp.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Word.cmp.fin
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/bool.bend&name=false_ne_true