TS001L — equal_remainder_affine_values_balanced_congruent

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 i j q i2 j2 q2 t. r * i + j = p * q + t -> r * i2 + j2 = p * q2 + t -> (exists ftcn_left_prime_affine ftcn_right_prime_affine. (r * i + j) + (p) * ftcn_left_prime_affine = (r * i2 + j2) + (p) * ftcn_right_prime_affine)

Constructive proof overview

Generated structural guide

Equal witnessed affine remainders produce an actual balanced affine-congruence certificate.

The unchanged tactic script uses 1 declared prerequisite and contains 25 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

TS0010 equal_affine_remainders_balanced

Direct dependents

TS001N prime_floor_affine_grid_collision_represents_prime

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

25 script commands · 5 reading checkpoints · 0 local claims

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)

equal affine remainders balanced

01Fix variables and assumptionsL1–10

Work with arbitrary variables or the premises of the current implication.