DL0039

matrix_rank_bounded_prefix_drop_last

Alpha v34 independently verified · alpha_closed; checked-use authorized; not Stable

Deleting the last index preserves a finite selector value bound.

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 l B. (forall fom_index_mrf_drop_source. (exists fom_gap_mrf_drop_source_index_bound. fom_gap_mrf_drop_source_index_bound + S (fom_index_mrf_drop_source) = S l) -> exists fom_value_mrf_drop_source. ((((exists fom_beta_height_mrf_drop_source_entry. fom_beta_height_mrf_drop_source_entry + S (fom_value_mrf_drop_source) = S ((S (fom_index_mrf_drop_source)) * c)) /\ exists fom_beta_quotient_mrf_drop_source_entry. b = fom_beta_quotient_mrf_drop_source_entry * S ((S (fom_index_mrf_drop_source)) * c) + (fom_value_mrf_drop_source))) /\ (exists fom_gap_mrf_drop_source_value_bound. fom_gap_mrf_drop_source_value_bound + S (fom_value_mrf_drop_source) = B))) -> (forall fom_index_mrf_drop_result. (exists fom_gap_mrf_drop_result_index_bound. fom_gap_mrf_drop_result_index_bound + S (fom_index_mrf_drop_result) = l) -> exists fom_value_mrf_drop_result. ((((exists fom_beta_height_mrf_drop_result_entry. fom_beta_height_mrf_drop_result_entry + S (fom_value_mrf_drop_result) = S ((S (fom_index_mrf_drop_result)) * c)) /\ exists fom_beta_quotient_mrf_drop_result_entry. b = fom_beta_quotient_mrf_drop_result_entry * S ((S (fom_index_mrf_drop_result)) * c) + (fom_value_mrf_drop_result))) /\ (exists fom_gap_mrf_drop_result_value_bound. fom_gap_mrf_drop_result_value_bound + S (fom_value_mrf_drop_result) = B)))

Constructive proof overview

Generated structural guide

Deleting the last index preserves a finite selector value bound.

The unchanged tactic script uses 1 declared prerequisite and contains 13 exact native proof lines.

Alpha v34 checked-use · first admitted v27 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

le_succ Stable theorem; checked-use authorized

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

13 script commands · 2 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.

01Fix variables and assumptionsL1–7

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

  1. L1
    intro b
  2. L2
    intro c
  3. L3
    intro l
  4. L4
    intro B
  5. L5
    intro hbounded
  6. L6
    intro i
  7. L7
    intro hi
02Use earlier factsL8–13

Instantiate or apply named facts and discharge the corresponding proof obligations.

  1. L8
    specialize hbounded (i)
  2. L9
    apply hbounded
  3. L10
    specialize le_succ (S i)
  4. L11
    specialize le_succ (l)
  5. L12
    apply le_succ
  6. L13
    exact hi

Library-wide reading audit

Original exact command ledger · 13 lines
  1. 0001intro b
  2. 0002intro c
  3. 0003intro l
  4. 0004intro B
  5. 0005intro hbounded
  6. 0006intro i
  7. 0007intro hi
  8. 0008specialize hbounded (i)
  9. 0009apply hbounded
  10. 0010specialize le_succ (S i)
  11. 0011specialize le_succ (l)
  12. 0012apply le_succ
  13. 0013exact hi