def lt_le

bend-collections-laws-math@1.0.0.0 · proofs/lib/nat.bend:96

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

96def lt_le(+a: Nat, +b: Nat, e: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_le(a, b) == True{} : Bool}:
97  match a b:
98    case 0n 0n:
99      {==}
100    case 0n 1n+q:
101      {==}
102    case 1n+p 0n:
103      Empty.absurd({Nat.is_le(1n+p, 0n) == True{} : Bool}, L.false_true(e))
104    case 1n+p 1n+q:
105      lt_le(p, q, e)