GF0085

gaussian_product_beta_value_transport

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

Equality of factor codes transports both boundedness and the actual beta remainder equation.

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 i a d. a=d -> (((exists ff_h_gprod_value_transport_source. ff_h_gprod_value_transport_source + S (a) = S ((S (i)) * c)) /\ exists ff_q_gprod_value_transport_source. b = ff_q_gprod_value_transport_source * S ((S (i)) * c) + (a))) -> (((exists ff_h_gprod_value_transport_target. ff_h_gprod_value_transport_target + S (d) = S ((S (i)) * c)) /\ exists ff_q_gprod_value_transport_target. b = ff_q_gprod_value_transport_target * S ((S (i)) * c) + (d)))

Constructive proof overview

Generated structural guide

Equality of factor codes transports both boundedness and the actual beta remainder equation.

The unchanged tactic script uses 0 declared prerequisites and contains 10 exact native proof lines.

Alpha v34 checked-use · first admitted v30 · 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

10 script commands · 3 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 i
  4. L4
    intro a
  5. L5
    intro d
  6. L6
    intro heq
  7. L7
    intro h
02Calculate and transport equalitiesL8–9

Carry out the recorded arithmetic or equality steps; inspect the exact commands for their direction and premises.

  1. L8
    rewrite heq at h
  2. L9
    rewrite heq at h
03Use earlier factsL10–10

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

  1. L10
    exact h

Library-wide reading audit

Original exact command ledger · 10 lines
  1. 0001intro b
  2. 0002intro c
  3. 0003intro i
  4. 0004intro a
  5. 0005intro d
  6. 0006intro heq
  7. 0007intro h
  8. 0008rewrite heq at h
  9. 0009rewrite heq at h
  10. 0010exact h