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 w rb rc cb cc q ub uc. (forall mdr_i_empty_prefix. (exists mdr_gap_empty_prefixbound. mdr_gap_empty_prefixbound + S (mdr_i_empty_prefix) = (0)) -> exists mdr_a_empty_prefix. (((exists mdr_r_empty_prefixpoint mdr_s_empty_prefixpoint mdr_u_empty_prefixpoint mdr_v_empty_prefixpoint. ((mdr_i_empty_prefix = (q) * mdr_r_empty_prefixpoint + mdr_s_empty_prefixpoint) /\ ((exists mdr_gap_empty_prefixpointcolumn. mdr_gap_empty_prefixpointcolumn + S (mdr_s_empty_prefixpoint) = (q)) /\ ((((exists ff_h_mdr_empty_prefixpointrow_index. ff_h_mdr_empty_prefixpointrow_index + S (mdr_u_empty_prefixpoint) = S ((S (mdr_r_empty_prefixpoint)) * rc)) /\ exists ff_q_mdr_empty_prefixpointrow_index. rb = ff_q_mdr_empty_prefixpointrow_index * S ((S (mdr_r_empty_prefixpoint)) * rc) + (mdr_u_empty_prefixpoint))) /\ ((((exists ff_h_mdr_empty_prefixpointcolumn_index. ff_h_mdr_empty_prefixpointcolumn_index + S (mdr_v_empty_prefixpoint) = S ((S (mdr_s_empty_prefixpoint)) * cc)) /\ exists ff_q_mdr_empty_prefixpointcolumn_index. cb = ff_q_mdr_empty_prefixpointcolumn_index * S ((S (mdr_s_empty_prefixpoint)) * cc) + (mdr_v_empty_prefixpoint))) /\ (((exists ff_h_mdr_empty_prefixpointsource. ff_h_mdr_empty_prefixpointsource + S (mdr_a_empty_prefix) = S ((S ((mdr_u_empty_prefixpoint) * (w) + (mdr_v_empty_prefixpoint))) * c)) /\ exists ff_q_mdr_empty_prefixpointsource. b = ff_q_mdr_empty_prefixpointsource * S ((S ((mdr_u_empty_prefixpoint) * (w) + (mdr_v_empty_prefixpoint))) * c) + (mdr_a_empty_prefix)))))))) /\ (((exists ff_h_mdr_empty_prefixoutput. ff_h_mdr_empty_prefixoutput + S (mdr_a_empty_prefix) = S ((S (mdr_i_empty_prefix)) * uc)) /\ exists ff_q_mdr_empty_prefixoutput. ub = ff_q_mdr_empty_prefixoutput * S ((S (mdr_i_empty_prefix)) * uc) + (mdr_a_empty_prefix))))))Constructive proof overview
Generated structural guide
Every code witnesses the actual selected-submatrix prefix of length zero.
The unchanged tactic script uses 1 declared prerequisite and contains 16 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 assumptionsL1–10
02Fix variables and assumptionsL11–12
03Separate the logical casesL13–13
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L13
exfalso