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 p r. p = S r -> exists gs_u_square gs_v_square. (r * r) + p * gs_u_square = (1) + p * gs_v_squareStructural proof guide
Generated structural guide
The predecessor of a successor squares to one modulo that successor.
Use the direct prerequisites mul_one, mul_succ_left, add_assoc, add_comm, zero_add, add_succ_left as previously established PA formulas.
The proof proceeds by equality transport (2), certified simplification (1).
Referenced ingredients
Proof neighborhood
Direct dependencies
PA0002 mul_one PA000G mul_succ_left PA0009 add_assoc PA000F add_comm PA0001 zero_add PA000E add_succ_leftDirect 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.