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 fslb_bounded_prime_bridge fslb_bounded_multiplier_bridge. ((~(fslb_bounded_prime_bridge = 1) /\ forall frm_prime_left_fslb_bounded_prime_bridge frm_prime_right_fslb_bounded_prime_bridge. fslb_bounded_prime_bridge = frm_prime_left_fslb_bounded_prime_bridge * frm_prime_right_fslb_bounded_prime_bridge -> frm_prime_left_fslb_bounded_prime_bridge = 1 \/ frm_prime_right_fslb_bounded_prime_bridge = 1)) -> ~(fslb_bounded_multiplier_bridge = 0) -> ~(fslb_bounded_multiplier_bridge = 1) -> (exists fslb_bounded_upper_gap_bridge. fslb_bounded_upper_gap_bridge + S fslb_bounded_multiplier_bridge = fslb_bounded_prime_bridge) -> (exists fsl_a_fslb_bounded_source_bridge fsl_b_fslb_bounded_source_bridge fsl_c_fslb_bounded_source_bridge fsl_d_fslb_bounded_source_bridge. (fslb_bounded_prime_bridge * fslb_bounded_multiplier_bridge) = fsl_a_fslb_bounded_source_bridge * fsl_a_fslb_bounded_source_bridge + fsl_b_fslb_bounded_source_bridge * fsl_b_fslb_bounded_source_bridge + fsl_c_fslb_bounded_source_bridge * fsl_c_fslb_bounded_source_bridge + fsl_d_fslb_bounded_source_bridge * fsl_d_fslb_bounded_source_bridge) -> exists fslb_bounded_smaller_bridge. (~(fslb_bounded_smaller_bridge = 0) /\ ((exists fslb_bounded_lower_gap_bridge. fslb_bounded_lower_gap_bridge + S fslb_bounded_smaller_bridge = fslb_bounded_multiplier_bridge) /\ (exists fsl_a_fslb_bounded_target_bridge fsl_b_fslb_bounded_target_bridge fsl_c_fslb_bounded_target_bridge fsl_d_fslb_bounded_target_bridge. (fslb_bounded_prime_bridge * fslb_bounded_smaller_bridge) = fsl_a_fslb_bounded_target_bridge * fsl_a_fslb_bounded_target_bridge + fsl_b_fslb_bounded_target_bridge * fsl_b_fslb_bounded_target_bridge + fsl_c_fslb_bounded_target_bridge * fsl_c_fslb_bounded_target_bridge + fsl_d_fslb_bounded_target_bridge * fsl_d_fslb_bounded_target_bridge)))) -> forall n. (exists fsl_a_fslb_natural_result fsl_b_fslb_natural_result fsl_c_fslb_natural_result fsl_d_fslb_natural_result. (n) = fsl_a_fslb_natural_result * fsl_a_fslb_natural_result + fsl_b_fslb_natural_result * fsl_b_fslb_natural_result + fsl_c_fslb_natural_result * fsl_c_fslb_natural_result + fsl_d_fslb_natural_result * fsl_d_fslb_natural_result)Constructive proof overview
Generated structural guide
The complete all-natural Lagrange conclusion follows from exactly the sharp bounded strict-multiplier descent hypothesis, with every prime seed already constructed.
The unchanged tactic script uses 2 declared prerequisites and contains 4 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 (2)
01Fix variables and assumptionsL1–1
Work with arbitrary variables or the premises of the current implication.
- L1
intro hstep
Original exact command ledger · 4 lines
- 0001
intro hstep - 0002
apply four_square_lagrange_from_all_primes - 0003
apply four_square_prime_from_bounded_strict_descent - 0004
exact hstep