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
forall p x y. x * x + y * y + 1 = p -> (exists fsl_a_prime fsl_b_prime fsl_c_prime fsl_d_prime. (p) = fsl_a_prime * fsl_a_prime + fsl_b_prime * fsl_b_prime + fsl_c_prime * fsl_c_prime + fsl_d_prime * fsl_d_prime)Every purple notation token opens its conservative definition. This reading surface never changes the unchanged intuitionistic kernel or confers checked-use authority.
Definitions used by this theorem
In the theorem statement
In local proof propositions
Exact expanded first-order statement
forall p x y. x * x + y * y + 1 = p -> (exists fsl_a_prime fsl_b_prime fsl_c_prime fsl_d_prime. (p) = fsl_a_prime * fsl_a_prime + fsl_b_prime * fsl_b_prime + fsl_c_prime * fsl_c_prime + fsl_d_prime * fsl_d_prime)Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only propositions whose conservative expansion has been checked for exact first-order equivalence are compacted. Every changed line retains its immutable exact replay 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.