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 b c B. (forall fom_index_mrf_empty_bounded. (exists fom_gap_mrf_empty_bounded_index_bound. fom_gap_mrf_empty_bounded_index_bound + S (fom_index_mrf_empty_bounded) = 0) -> exists fom_value_mrf_empty_bounded. ((((exists fom_beta_height_mrf_empty_bounded_entry. fom_beta_height_mrf_empty_bounded_entry + S (fom_value_mrf_empty_bounded) = S ((S (fom_index_mrf_empty_bounded)) * c)) /\ exists fom_beta_quotient_mrf_empty_bounded_entry. b = fom_beta_quotient_mrf_empty_bounded_entry * S ((S (fom_index_mrf_empty_bounded)) * c) + (fom_value_mrf_empty_bounded))) /\ (exists fom_gap_mrf_empty_bounded_value_bound. fom_gap_mrf_empty_bounded_value_bound + S (fom_value_mrf_empty_bounded) = B)))Constructive proof overview
Generated structural guide
Every beta code describes the empty bounded selector prefix.
The unchanged tactic script uses 1 declared prerequisite and contains 9 exact native proof lines.
Alpha v34 checked-use · first admitted v27 · independently kernel and Lean verified; not Stable
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 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.
Named ingredients (1)
01Fix variables and assumptionsL1–5
02Separate the logical casesL6–6
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L6
exfalso