def double_lt

bend-collections-laws-math@1.0.0.0 · proofs/lib/nat.bend:383

import Base

383def double_lt(+a: Nat, +b: Nat, e: {Nat.is_lt(a, b) == True{} : Bool}) -> {Nat.is_lt(Nat.double(a), Nat.double(b)) == True{} : Bool}:
384  match a b:
385    case _ 0n:
386      Empty.absurd({Nat.is_lt(Nat.double(a), 0n) == True{} : Bool}, lt_zero_absurd(a, e))
387    case 0n 1n+q:
388      {==}
389    case 1n+p 1n+q:
390      double_lt(p, q, e)