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. (exists pmt_even_n. n = 2 * pmt_even_n) -> (exists pmt_u_n_zero pmt_v_n_zero. n + 2 * pmt_u_n_zero = 0 + 2 * pmt_v_n_zero)Structural proof guide
Generated structural guide
Every even natural is congruent to zero modulo two.
Use the direct prerequisites dvd_to_mod_zero as previously established PA formulas.
The proof proceeds by direct introduction and elimination.
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 Alpha-v25 checked-use theorem is independently kernel-checked when replayed; it is not a Stable theorem.
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.