def double_le

bend-collections-laws-math@1.0.0.0 · proofs/lib/nat.bend:392

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

392def double_le(+a: Nat, +b: Nat, e: {Nat.is_le(a, b) == True{} : Bool}) -> {Nat.is_le(Nat.double(a), Nat.double(b)) == True{} : Bool}:
393  match a b:
394    case 0n _:
395      zero_le(Nat.double(b))
396    case 1n+p 0n:
397      Empty.absurd({Nat.is_le(Nat.double(1n+p), 0n) == True{} : Bool}, L.false_true(e))
398    case 1n+p 1n+q:
399      double_le(p, q, e)