JT001A

jordan_tuple_listed_empty

Alpha v35 independently verified · alpha_closed; checked-use authorized; not Stable

An empty actual outer list contains no representative.

Exact expanded first-order arithmetic statement

forall b c k B C D E. ~(exists jt_index_listedempty jt_code_listedempty jt_scale_listedempty. ((exists jt_gap_listedemptyindex. jt_gap_listedemptyindex+S (jt_index_listedempty)=(0)) /\ (((((((exists fs_h_jt_listedemptycode. fs_h_jt_listedemptycode + S (jt_code_listedempty) = S ((S (jt_index_listedempty)) * C)) /\ exists fs_q_jt_listedemptycode. B = fs_q_jt_listedemptycode * S ((S (jt_index_listedempty)) * C) + (jt_code_listedempty))) /\ (((exists fs_h_jt_listedemptyscale. fs_h_jt_listedemptyscale + S (jt_scale_listedempty) = S ((S (jt_index_listedempty)) * E)) /\ exists fs_q_jt_listedemptyscale. D = fs_q_jt_listedemptyscale * S ((S (jt_index_listedempty)) * E) + (jt_scale_listedempty))))) /\ (forall jt_index_listedemptyequal jt_left_listedemptyequal jt_right_listedemptyequal. (exists jt_gap_listedemptyequalindex. jt_gap_listedemptyequalindex+S (jt_index_listedemptyequal)=(k)) -> (((exists fs_h_jt_listedemptyequalleft. fs_h_jt_listedemptyequalleft + S (jt_left_listedemptyequal) = S ((S (jt_index_listedemptyequal)) * c)) /\ exists fs_q_jt_listedemptyequalleft. b = fs_q_jt_listedemptyequalleft * S ((S (jt_index_listedemptyequal)) * c) + (jt_left_listedemptyequal))) -> (((exists fs_h_jt_listedemptyequalright. fs_h_jt_listedemptyequalright + S (jt_right_listedemptyequal) = S ((S (jt_index_listedemptyequal)) * jt_scale_listedempty)) /\ exists fs_q_jt_listedemptyequalright. jt_code_listedempty = fs_q_jt_listedemptyequalright * S ((S (jt_index_listedemptyequal)) * jt_scale_listedempty) + (jt_right_listedemptyequal))) -> jt_left_listedemptyequal=jt_right_listedemptyequal)))))

Constructive proof overview

Generated structural guide

An empty actual outer list contains no representative.

The unchanged tactic script uses 2 declared prerequisites and contains 19 exact native proof lines.

Alpha v35 checked-use · first admitted v35 · independently kernel and Lean verified; not Stable

Proof neighborhood

Direct dependencies

lt_not_le Alpha theorem; checked-use authorized zero_le Alpha theorem; checked-use authorized

Direct dependents

JT001C jordan_tuple_listed_decidable

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

19 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 assumptionsL1–8

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

  1. L1
    intro b
  2. L2
    intro c
  3. L3
    intro k
  4. L4
    intro B
  5. L5
    intro C
  6. L6
    intro D
  7. L7
    intro E
  8. L8
    intro h
02Separate the logical casesL9–13

Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.

  1. L9
    cases h
  2. L10
    cases h_witness
  3. L11
    cases h_witness_witness
  4. L12
    cases h_witness_witness_witness
  5. L13
    cases h_witness_witness_witness_right
03Use earlier factsL14–19

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

  1. L14
    specialize lt_not_le (x)
  2. L15
    specialize lt_not_le (0)
  3. L16
    apply lt_not_le
  4. L17
    exact h_witness_witness_witness_left
  5. L18
    specialize zero_le (x)
  6. L19
    apply zero_le

Library-wide reading audit

Original exact command ledger · 19 lines
  1. 0001intro b
  2. 0002intro c
  3. 0003intro k
  4. 0004intro B
  5. 0005intro C
  6. 0006intro D
  7. 0007intro E
  8. 0008intro h
  9. 0009cases h
  10. 0010cases h_witness
  11. 0011cases h_witness_witness
  12. 0012cases h_witness_witness_witness
  13. 0013cases h_witness_witness_witness_right
  14. 0014specialize lt_not_le (x)
  15. 0015specialize lt_not_le (0)
  16. 0016apply lt_not_le
  17. 0017exact h_witness_witness_witness_left
  18. 0018specialize zero_le (x)
  19. 0019apply zero_le