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_selector_emptybound. (exists fom_gap_mrf_selector_emptybound_index_bound. fom_gap_mrf_selector_emptybound_index_bound + S (fom_index_mrf_selector_emptybound) = 0) -> exists fom_value_mrf_selector_emptybound. ((((exists fom_beta_height_mrf_selector_emptybound_entry. fom_beta_height_mrf_selector_emptybound_entry + S (fom_value_mrf_selector_emptybound) = S ((S (fom_index_mrf_selector_emptybound)) * c)) /\ exists fom_beta_quotient_mrf_selector_emptybound_entry. b = fom_beta_quotient_mrf_selector_emptybound_entry * S ((S (fom_index_mrf_selector_emptybound)) * c) + (fom_value_mrf_selector_emptybound))) /\ (exists fom_gap_mrf_selector_emptybound_value_bound. fom_gap_mrf_selector_emptybound_value_bound + S (fom_value_mrf_selector_emptybound) = B))) /\ (forall mdr_i_selector_emptydistinct mdr_j_selector_emptydistinct mdr_a_selector_emptydistinct. (exists mdr_gap_selector_emptydistincti. mdr_gap_selector_emptydistincti + S (mdr_i_selector_emptydistinct) = (0)) -> (exists mdr_gap_selector_emptydistinctj. mdr_gap_selector_emptydistinctj + S (mdr_j_selector_emptydistinct) = (0)) -> (((exists ff_h_mdr_selector_emptydistinctfirst. ff_h_mdr_selector_emptydistinctfirst + S (mdr_a_selector_emptydistinct) = S ((S (mdr_i_selector_emptydistinct)) * c)) /\ exists ff_q_mdr_selector_emptydistinctfirst. b = ff_q_mdr_selector_emptydistinctfirst * S ((S (mdr_i_selector_emptydistinct)) * c) + (mdr_a_selector_emptydistinct))) -> (((exists ff_h_mdr_selector_emptydistinctsecond. ff_h_mdr_selector_emptydistinctsecond + S (mdr_a_selector_emptydistinct) = S ((S (mdr_j_selector_emptydistinct)) * c)) /\ exists ff_q_mdr_selector_emptydistinctsecond. b = ff_q_mdr_selector_emptydistinctsecond * S ((S (mdr_j_selector_emptydistinct)) * c) + (mdr_a_selector_emptydistinct))) -> mdr_i_selector_emptydistinct = mdr_j_selector_emptydistinct)))Constructive proof overview
Generated structural guide
The empty row or column selector is valid even when its ambient dimension is zero.
The unchanged tactic script uses 2 declared prerequisites and contains 19 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 (2)
01Fix variables and assumptionsL1–3
02Separate the logical casesL4–4
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L4
split
03Use earlier factsL5–8
04Fix variables and assumptionsL9–15
05Separate the logical casesL16–16
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L16
exfalso
Original exact command ledger · 19 lines
- 0001
intro b - 0002
intro c - 0003
intro B - 0004
split - 0005
specialize matrix_rank_bounded_prefix_empty (b) - 0006
specialize matrix_rank_bounded_prefix_empty (c) - 0007
specialize matrix_rank_bounded_prefix_empty (B) - 0008
apply matrix_rank_bounded_prefix_empty - 0009
intro i - 0010
intro j - 0011
intro a - 0012
intro hi - 0013
intro hj - 0014
intro ha - 0015
intro hb - 0016
exfalso - 0017
specialize matrix_rank_no_index_below_zero (i) - 0018
apply matrix_rank_no_index_below_zero - 0019
exact hi