ProofShift.ns.lt_one: def of bend-osdev-word64@0.1.1.0
Import: import bend-osdev-word64@0.1.1.0/proof_shift.bend as ProofShift
Lines 102-107 of bend-osdev-word64@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-word64@0.1.1.0/proof_shift.bend&start_line=102&end_line=107

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

def ns.lt_one(x: Nat, e: {Nat.is_lt(x, 1n) == True{} : Bool}) -> {x == 0n : Nat}:
  match x:
    case 0n:
      {==}
    case 1n+ +p:
      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)))

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.ft
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-word64@0.1.1.0/proof_value.bend&name=wn.not_lt_zero