DL0002

matrix_recursive_prefix_refl

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

A beta prefix is unchanged under its own exact code pair.

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. (forall mdr_i_refl mdr_a_refl. (exists mdr_gap_reflb. mdr_gap_reflb + S (mdr_i_refl) = (l)) -> (((exists ff_h_mdr_reflo. ff_h_mdr_reflo + S (mdr_a_refl) = S ((S (mdr_i_refl)) * c)) /\ exists ff_q_mdr_reflo. b = ff_q_mdr_reflo * S ((S (mdr_i_refl)) * c) + (mdr_a_refl))) -> (((exists ff_h_mdr_refln. ff_h_mdr_refln + S (mdr_a_refl) = S ((S (mdr_i_refl)) * c)) /\ exists ff_q_mdr_refln. b = ff_q_mdr_refln * S ((S (mdr_i_refl)) * c) + (mdr_a_refl))))

Constructive proof overview

Generated structural guide

A beta prefix is unchanged under its own exact code pair.

The unchanged tactic script uses 0 declared prerequisites and contains 8 exact native proof lines.

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

Proof neighborhood

Direct dependencies

none

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

8 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 i
  5. L5
    intro a
  6. L6
    intro hi
  7. L7
    intro ha
02Use earlier factsL8–8

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

  1. L8
    exact ha

Library-wide reading audit

Original exact command ledger · 8 lines
  1. 0001intro b
  2. 0002intro c
  3. 0003intro l
  4. 0004intro i
  5. 0005intro a
  6. 0006intro hi
  7. 0007intro ha
  8. 0008exact ha