def double_le

stelliferous@0.0.2.0 · proofs/nat_order.bend:196

import Base
import stelliferous@0.0.2.0/proofs/word_encoding.bend as WordEncoding

196def double_le(+a: Nat,+b: Nat,ordered: {Nat.is_le(a,b) == True{} : Bool}) -> {Nat.is_le(Nat.double(a),Nat.double(b)) == True{} : Bool}:
197  match a b:
198    case 0n b: zero_le(Nat.double(b))
199    case 1n+a 0n: Empty.absurd({Nat.is_le(Nat.double(1n+a),0n) == True{} : Bool},WordEncoding.false_true(ordered))
200    case 1n+a 1n+b: double_le(a,b,ordered)