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.
Statement with defined notation
∀ p. ∀ r. p = S r → BalancedInverse(p,r,r)Every purple notation token opens its conservative definition. This is a reading surface; the compiler expands the statement before the unchanged kernel checks it.
Definitions used by this theorem
In the theorem statement
1 occurrences
In local proof propositions
0 occurrences
Exact expanded native-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_squareProof neighborhood
Direct theorem prerequisites
PA0002 mul_one PA000G mul_succ_left PA0009 add_assoc PA000F add_comm PA0001 zero_add PA000E add_succ_leftDirect theorem dependents
Definition-aware tactic body
Only local propositions introduced by have or suffices are compacted. The untrusted compiler re-expands each one before the original tactic script is replayed; defined notation is never accepted by the kernel. Open the exact replay line beneath every changed command.
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.