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. Prime(p) → p = 2 ∨ Mod4One(p) → ∃ x. ∃ y. ∃ z. ∃ n. p = x · x + y · y + z · z + n · nEvery 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. ((~(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)Proof neighborhood
Direct theorem prerequisites
FS003D four_square_two_square_embeddingDirect 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.