BA0002

cf_approximation_prepend_determinant_backward

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

The reverse determinant orientation has the same actual quotient-matrix transition.

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 u U v V q. U * v + 1 = u * V -> (q * u + v) * U + 1 = (q * U + V) * u

Constructive proof overview

Generated structural guide

The reverse determinant orientation has the same actual quotient-matrix transition.

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

Alpha v34 checked-use · first admitted v29 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

BA0001 cf_approximation_prepend_determinant_forward

Direct dependents

BA0006 cf_approximation_prepend_identity

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.

Named ingredients (1)
cf approximation prepend determinant forward
01Fix variables and assumptionsL1–6

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

  1. L1
    intro u
  2. L2
    intro U
  3. L3
    intro v
  4. L4
    intro V
  5. L5
    intro q
  6. L6
    intro hd
02Use earlier factsL7–13

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

  1. L7
    specialize cf_approximation_prepend_determinant_forward (U)
  2. L8
    specialize cf_approximation_prepend_determinant_forward (u)
  3. L9
    specialize cf_approximation_prepend_determinant_forward (V)
  4. L10
    specialize cf_approximation_prepend_determinant_forward (v)
  5. L11
    specialize cf_approximation_prepend_determinant_forward (q)
  6. L12
    apply cf_approximation_prepend_determinant_forward
  7. L13
    exact hd

Library-wide reading audit

Original exact command ledger · 13 lines
  1. 0001intro u
  2. 0002intro U
  3. 0003intro v
  4. 0004intro V
  5. 0005intro q
  6. 0006intro hd
  7. 0007specialize cf_approximation_prepend_determinant_forward (U)
  8. 0008specialize cf_approximation_prepend_determinant_forward (u)
  9. 0009specialize cf_approximation_prepend_determinant_forward (V)
  10. 0010specialize cf_approximation_prepend_determinant_forward (v)
  11. 0011specialize cf_approximation_prepend_determinant_forward (q)
  12. 0012apply cf_approximation_prepend_determinant_forward
  13. 0013exact hd