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 a z q r c s. z = a * q + r -> r * r = a * c + s -> z * z = a * ((q * z + r * q) + c) + sStructural proof guide
Generated structural guide
Lift one quotient-and-remainder equation through squaring.
Use the direct prerequisites square_decomp, add_residue 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 (2)
01Fix variables and assumptionsL1–8
02Calculate and transport equalitiesL9–9
Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.
- L9
trans a * (q * z + r * q) + r * r