def uq.lt_dbl_self

bend-osdev-algo@0.1.0.0 · proof_u32.bend:187

import Base

187def uq.lt_dbl_self(x: Nat, y: Nat, h: {Nat.is_lt(x, y) == True{} : Bool}) -> {Nat.is_lt(x, Nat.double(y)) == True{} : Bool}:
188  match x y:
189    case 0n 0n:
190      Empty.absurd({Nat.is_lt(0n, 0n) == True{} : Bool}, uq.ft(h))
191    case 0n 1n+yp:
192      {==}
193    case 1n+xp 0n:
194      Empty.absurd({Nat.is_lt(1n+xp, 0n) == True{} : Bool}, uq.ft(h))
195    case 1n+ +xp 1n+ +yp:
196      uq.lt_succ_r(xp, Nat.double(yp), uq.lt_dbl_self(xp, yp, h))