def ns.lt_one

bend-osdev-word64@0.1.1.0 · proof_shift.bend:102

import Base
import bend-osdev-word64@0.1.1.0/proof_value.bend as P

102def ns.lt_one(x: Nat, e: {Nat.is_lt(x, 1n) == True{} : Bool}) -> {x == 0n : Nat}:
103  match x:
104    case 0n:
105      {==}
106    case 1n+ +p:
107      Empty.absurd({1n+p == 0n : Nat}, P.wn.ft(Equal.trans(Bool, False{}, Nat.is_lt(p, 0n), True{}, P.wn.not_lt_zero(p), e)))