JT0017

jordan_tuple_equal_drop_last

Restrict coordinate equality to the actual predecessor prefix.

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

95 new Alpha admissions come from 96 source lemmas: tuple equality reflexivity reuses an already-admitted theorem and is not counted twice. All counts use actual finite beta-coded enumerations. G008 multiplicativity is proved; the general prime-power count and distinct-prime product formula are further goals. General prime-power fields (G091) remain open. Stable is unchanged.

Exact theorem in conservative defined notation

∀ b. ∀ c. ∀ d. ∀ e. ∀ k. IntegerVectorZero(b,c,d,e,S k) → IntegerVectorZero(b,c,d,e,k)

Every linked abbreviation expands hygienically to the identical original native formula.

Definition DAG

IntegerVectorZero(ab,ac,db,dc,l) · 2

Actual proof prerequisites

le_succ · checked external prerequisite
Original expanded first-order statement 
forall b c d e k. (forall jt_index_eqdropsource jt_left_eqdropsource jt_right_eqdropsource. (exists jt_gap_eqdropsourceindex. jt_gap_eqdropsourceindex+S (jt_index_eqdropsource)=(S k)) -> (((exists fs_h_jt_eqdropsourceleft. fs_h_jt_eqdropsourceleft + S (jt_left_eqdropsource) = S ((S (jt_index_eqdropsource)) * c)) /\ exists fs_q_jt_eqdropsourceleft. b = fs_q_jt_eqdropsourceleft * S ((S (jt_index_eqdropsource)) * c) + (jt_left_eqdropsource))) -> (((exists fs_h_jt_eqdropsourceright. fs_h_jt_eqdropsourceright + S (jt_right_eqdropsource) = S ((S (jt_index_eqdropsource)) * e)) /\ exists fs_q_jt_eqdropsourceright. d = fs_q_jt_eqdropsourceright * S ((S (jt_index_eqdropsource)) * e) + (jt_right_eqdropsource))) -> jt_left_eqdropsource=jt_right_eqdropsource) -> (forall jt_index_eqdroptarget jt_left_eqdroptarget jt_right_eqdroptarget. (exists jt_gap_eqdroptargetindex. jt_gap_eqdroptargetindex+S (jt_index_eqdroptarget)=(k)) -> (((exists fs_h_jt_eqdroptargetleft. fs_h_jt_eqdroptargetleft + S (jt_left_eqdroptarget) = S ((S (jt_index_eqdroptarget)) * c)) /\ exists fs_q_jt_eqdroptargetleft. b = fs_q_jt_eqdroptargetleft * S ((S (jt_index_eqdroptarget)) * c) + (jt_left_eqdroptarget))) -> (((exists fs_h_jt_eqdroptargetright. fs_h_jt_eqdroptargetright + S (jt_right_eqdroptarget) = S ((S (jt_index_eqdroptarget)) * e)) /\ exists fs_q_jt_eqdroptargetright. d = fs_q_jt_eqdroptargetright * S ((S (jt_index_eqdroptarget)) * e) + (jt_right_eqdroptarget))) -> jt_left_eqdroptarget=jt_right_eqdroptarget)

Complete tactic proof in conservative notation

All 22 original proof lines are preserved. Only local proposition formulas are abbreviated; every abbreviation has an exact binder-safe expansion check. The linked exact edition contains the unchanged replay script.

Read the argument

Proof checkpoints

22 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.

Definition notation is shown below. Open the paired exact edition for the original native formulas. Source pairing is not a new equivalence certificate.

01Fix variables and assumptionsL1–10

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

  1. L1
    intro b
  2. L2
    intro c
  3. L3
    intro d
  4. L4
    intro e
  5. L5
    intro k
  6. L6
    intro h
  7. L7
    intro i
  8. L8
    intro a
  9. L9
    intro z
  10. L10
    intro hi
02Fix variables and assumptionsL11–12

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

  1. L11
    intro ha
  2. L12
    intro hz
03Use earlier factsL13–22

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

  1. L13
    specialize h (i)
  2. L14
    specialize h (a)
  3. L15
    specialize h (z)
  4. L16
    apply h
  5. L17
    specialize le_succ (S i)
  6. L18
    specialize le_succ (k)
  7. L19
    apply le_succ
  8. L20
    exact hi
  9. L21
    exact ha
  10. L22
    exact hz

Library-wide reading audit

Original defined command ledger · 22 lines
  1. 0001intro b
  2. 0002intro c
  3. 0003intro d
  4. 0004intro e
  5. 0005intro k
  6. 0006intro h
  7. 0007intro i
  8. 0008intro a
  9. 0009intro z
  10. 0010intro hi
  11. 0011intro ha
  12. 0012intro hz
  13. 0013specialize h (i)
  14. 0014specialize h (a)
  15. 0015specialize h (z)
  16. 0016apply h
  17. 0017specialize le_succ (S i)
  18. 0018specialize le_succ (k)
  19. 0019apply le_succ
  20. 0020exact hi
  21. 0021exact ha
  22. 0022exact hz