def h.fin_hd

bend-kit-collections@0.1.4.1 · PROOF.bend:1780

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

1780def h.fin_hd(t: Cmp, x: Bool, y: Bool, e: {Cmp.is_eq(Word.cmp.fin(x, y, t)) == True{} : Bool})
1781  -> {x == y : Bool}:
1782  match t:
1783    case LT{}:
1784      Empty.absurd({x == y : Bool}, MBool.false_ne_true()(e))
1785    case EQ{}:
1786      match x y:
1787        case False{} False{}:
1788          {==}
1789        case False{} True{}:
1790          Empty.absurd({False{} == True{} : Bool}, MBool.false_ne_true()(e))
1791        case True{} False{}:
1792          Empty.absurd({True{} == False{} : Bool}, MBool.false_ne_true()(e))
1793        case True{} True{}:
1794          {==}
1795    case GT{}:
1796      Empty.absurd({x == y : Bool}, MBool.false_ne_true()(e))