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. 1 <= n -> ~(n = 0)Structural proof guide
Generated structural guide
A natural at least one is nonzero.
This root lemma is proved directly from the PA rules and the hypotheses introduced by its statement.
The proof proceeds by case analysis (1), equality transport (2).
Referenced ingredients
Proof neighborhood
Direct dependencies
Direct dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Linked names are exact direct references. This Stable checked-use theorem is independently kernel-checked when replayed.
Read the argument
Proof checkpoints
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
02Separate the logical casesL4–4
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L4
cases h
03Calculate and transport equalitiesL5–5
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L5
rewrite hn at h_witness
04Use earlier factsL6–6
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L6
apply PA1
05Calculate and transport equalitiesL7–7
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L7
rewrite PA4 at h_witness
06Use earlier factsL8–8
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L8
exact h_witness