BT000J

le_antisymm

Stable checked-use theorem · independently kernel verified

The witness-defined order is antisymmetric.

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 PA statement

forall n m. n <= m -> m <= n -> n = m

Structural proof guide

The witness-defined order is antisymmetric.

Direct prerequisites: antisymm_from_witnesses. The authored body proceeds by case analysis (2).

Proof neighborhood

Direct dependencies

BT000I antisymm_from_witnesses

Direct dependents

BT00Q8 power_valuation_functional BT00QT prime_power_valuation_mul BT00WW bertrand_hj_base_window_thirty_two_from_total BT00YK no_bertrand_central_nonzero_valuation_factor_ranges

Formal native tactic body

Dependencies are hypotheses of the historical Alpha-v12 body receipt. The complete historical Alpha-v18 proof bundle independently checks every dependency; current Alpha v25 preserves that checked theorem use without changing Stable membership.

Read the argument

Proof checkpoints

9 script commands · 3 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.

Named ingredients (1)
antisymm from witnesses
01Fix variables and assumptionsL1–4

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

  1. L1
    intro n
  2. L2
    intro m
  3. L3
    intro h_nm
  4. L4
    intro h_mn
02Separate the logical casesL5–6

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L5
    cases h_nm
  2. L6
    cases h_mn
03Use earlier factsL7–9

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

  1. L7
    apply antisymm_from_witnesses
  2. L8
    exact h_nm_witness
  3. L9
    exact h_mn_witness

Library-wide reading audit

Original exact command ledger · 9 lines
  1. 0001intro n
  2. 0002intro m
  3. 0003intro h_nm
  4. 0004intro h_mn
  5. 0005cases h_nm
  6. 0006cases h_mn
  7. 0007apply antisymm_from_witnesses
  8. 0008exact h_nm_witness
  9. 0009exact h_mn_witness