CD0017

finite_bit_zero_one_conflict

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

The two characteristic-bit values are constructively distinct.

Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved. Exact original first-admission records.

Exact expanded first-order arithmetic statement

forall a. a=0 -> a=1 -> bot

Constructive proof overview

Generated structural guide

The two characteristic-bit values are constructively distinct.

The unchanged tactic script uses 1 declared prerequisite and contains 9 exact native proof lines.

Alpha v34 checked-use · first admitted v27 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

succ_ne_zero Stable theorem; checked-use authorized

Direct dependents

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply Stable membership.

Read the argument

Proof checkpoints

9 script commands · 4 reading checkpoints · 0 local claims

This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.

01Fix variables and assumptionsL1–3

Work with arbitrary variables or the premises of the current implication.

  1. L1
    intro a
  2. L2
    intro hz
  3. L3
    intro ho
02Use earlier factsL4–5

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L4
    specialize succ_ne_zero 0
  2. L5
    apply succ_ne_zero
03Calculate and transport equalitiesL6–7

Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.

  1. L6
    trans a
  2. L7
    symm
04Use earlier factsL8–9

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L8
    exact ho
  2. L9
    exact hz

Library-wide reading audit

Original exact command ledger · 9 lines
  1. 0001intro a
  2. 0002intro hz
  3. 0003intro ho
  4. 0004specialize succ_ne_zero 0
  5. 0005apply succ_ne_zero
  6. 0006trans a
  7. 0007symm
  8. 0008exact ho
  9. 0009exact hz