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 first-order arithmetic statement
forall p. ((~(p = 1) /\ forall frm_prime_left_fsl_prime frm_prime_right_fsl_prime. p = frm_prime_left_fsl_prime * frm_prime_right_fsl_prime -> frm_prime_left_fsl_prime = 1 \/ frm_prime_right_fsl_prime = 1)) -> (p = 2 \/ exists k. p = 4 * k + 1) -> (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)Constructive proof overview
Generated structural guide
The exceptional prime two and every prime congruent to one modulo four already have explicit four-square witnesses.
The unchanged tactic script uses 2 declared prerequisites and contains 8 exact native proof lines.
dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged
Proof neighborhood
Direct dependencies
prime_two_or_one_mod_four_is_sum_of_two_squares Alpha theorem; checked-use authorized FS003D four_square_two_square_embeddingDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This dependency-curried candidate body does not grant checked theorem use or Stable membership.
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.