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 m n xp yp xn yn. m * xp + n * yp = 1 + (m * xn + n * yn) -> exists u v. m * xp + n * u = (1 + m * xn) + n * vStructural proof guide
Generated structural guide
A balanced Bezout identity selects the left coefficient modulo the right modulus.
Use the direct prerequisites add_assoc 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 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.
Named ingredients (1)
01Fix variables and assumptionsL1–7
02Construct an explicit witnessL8–9
03Calculate and transport equalitiesL10–10
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L10
trans 1 + (m * xn + n * yn)
04Use earlier factsL11–11
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L11
exact h
05Calculate and transport equalitiesL12–12
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L12
symm
06Use earlier factsL13–13
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L13
apply add_assoc