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 n. (exists fsl_a_value fsl_b_value fsl_c_value fsl_d_value. (n) = fsl_a_value * fsl_a_value + fsl_b_value * fsl_b_value + fsl_c_value * fsl_c_value + fsl_d_value * fsl_d_value)) -> (forall fsl_three_prime_universal. ((~(fsl_three_prime_universal = 1) /\ forall frm_prime_left_fsl_three_universal frm_prime_right_fsl_three_universal. fsl_three_prime_universal = frm_prime_left_fsl_three_universal * frm_prime_right_fsl_three_universal -> frm_prime_left_fsl_three_universal = 1 \/ frm_prime_right_fsl_three_universal = 1)) -> (exists fsl_three_residue_universal. fsl_three_prime_universal = 4 * fsl_three_residue_universal + 3) -> (exists fsl_a_three_universal fsl_b_three_universal fsl_c_three_universal fsl_d_three_universal. (fsl_three_prime_universal) = fsl_a_three_universal * fsl_a_three_universal + fsl_b_three_universal * fsl_b_three_universal + fsl_c_three_universal * fsl_c_three_universal + fsl_d_three_universal * fsl_d_three_universal))) /\ ((forall fsl_three_prime_universal. ((~(fsl_three_prime_universal = 1) /\ forall frm_prime_left_fsl_three_universal frm_prime_right_fsl_three_universal. fsl_three_prime_universal = frm_prime_left_fsl_three_universal * frm_prime_right_fsl_three_universal -> frm_prime_left_fsl_three_universal = 1 \/ frm_prime_right_fsl_three_universal = 1)) -> (exists fsl_three_residue_universal. fsl_three_prime_universal = 4 * fsl_three_residue_universal + 3) -> (exists fsl_a_three_universal fsl_b_three_universal fsl_c_three_universal fsl_d_three_universal. (fsl_three_prime_universal) = fsl_a_three_universal * fsl_a_three_universal + fsl_b_three_universal * fsl_b_three_universal + fsl_c_three_universal * fsl_c_three_universal + fsl_d_three_universal * fsl_d_three_universal)) -> forall n. (exists fsl_a_value fsl_b_value fsl_c_value fsl_d_value. (n) = fsl_a_value * fsl_a_value + fsl_b_value * fsl_b_value + fsl_c_value * fsl_c_value + fsl_d_value * fsl_d_value)))Constructive proof overview
Generated structural guide
Universal Lagrange is constructively equivalent to the one unresolved family of three-modulo-four prime representations.
The unchanged tactic script uses 1 declared prerequisite 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
Direct 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.
Named ingredients (1)
01Separate the logical casesL1–1
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L1
split