def ge_false

stelliferous@0.0.2.0 · proofs/nat_order.bend:240

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

240def ge_false(+a: Nat,+b: Nat,h: {Nat.is_ge(a,b) == False{} : Bool}) -> {Nat.is_lt(a,b) == True{} : Bool}:
241  match a b:
242    case 0n 0n:
243      Empty.absurd({Nat.is_lt(0n,0n) == True{} : Bool},WordEncoding.false_true(Equal.sym(Bool,True{},False{},h)))
244    case 0n 1n+b:
245      {==}
246    case 1n+a 0n:
247      Empty.absurd({Nat.is_lt(1n+a,0n) == True{} : Bool},WordEncoding.false_true(Equal.sym(Bool,True{},False{},h)))
248    case 1n+a 1n+b:
249      ge_false(a,b,h)