Nat.eq_from_is_eq: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as Nat
Lines 223-232 of bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&start_line=223&end_line=232

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L

def eq_from_is_eq(+a: Nat, +b: Nat, e: {Nat.is_eq(a, b) == True{} : Bool}) -> {a == b : Nat}:
  match a b:
    case 0n 0n:
      {==}
    case 0n 1n+q:
      Empty.absurd({0n == 1n+q : Nat}, L.false_true(e))
    case 1n+p 0n:
      Empty.absurd({1n+p == 0n : Nat}, L.false_true(e))
    case 1n+p 1n+q:
      succ_cong(p, q, eq_from_is_eq(p, q, 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=Empty.absurd
  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-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_cong