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 r x y. (exists ftcn_left_linear ftcn_right_linear. (r * x) + (p) * ftcn_left_linear = (y) + (p) * ftcn_right_linear) -> (exists ftcn_left_squared ftcn_right_squared. ((r * x) * (r * x)) + (p) * ftcn_left_squared = (y * y) + (p) * ftcn_right_squared)Constructive proof overview
Generated structural guide
Balanced congruence respects squaring of a direct linear relation.
The unchanged tactic script uses 1 declared prerequisite and contains 13 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
mod_eq_mul Stable theorem; checked-use authorizedDirect dependents
Formal native tactic body
Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This exact body belongs to a complete independently kernel-checked constructive proof bundle and has Alpha checked-use authority; it does not imply 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.