JT0006

jordan_primitive_tuple_divisor_modulus

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

Primitivity descends from a modulus to a genuine divisor of it.

Exact expanded first-order arithmetic statement

forall n m b c k. (exists jt_factor_smalldivisor. (m)=(n)*jt_factor_smalldivisor) -> (forall jt_divisor_largemod. (exists jt_factor_largemodmodulus. (m)=(jt_divisor_largemod)*jt_factor_largemodmodulus) -> (forall jt_index_largemodcoordinates jt_value_largemodcoordinates. (exists jt_gap_largemodcoordinatesindex. jt_gap_largemodcoordinatesindex+S (jt_index_largemodcoordinates)=(k)) -> (((exists fs_h_jt_largemodcoordinatesat. fs_h_jt_largemodcoordinatesat + S (jt_value_largemodcoordinates) = S ((S (jt_index_largemodcoordinates)) * c)) /\ exists fs_q_jt_largemodcoordinatesat. b = fs_q_jt_largemodcoordinatesat * S ((S (jt_index_largemodcoordinates)) * c) + (jt_value_largemodcoordinates))) -> (exists jt_factor_largemodcoordinatesdivides. (jt_value_largemodcoordinates)=(jt_divisor_largemod)*jt_factor_largemodcoordinatesdivides)) -> jt_divisor_largemod=1) -> (forall jt_divisor_smallmod. (exists jt_factor_smallmodmodulus. (n)=(jt_divisor_smallmod)*jt_factor_smallmodmodulus) -> (forall jt_index_smallmodcoordinates jt_value_smallmodcoordinates. (exists jt_gap_smallmodcoordinatesindex. jt_gap_smallmodcoordinatesindex+S (jt_index_smallmodcoordinates)=(k)) -> (((exists fs_h_jt_smallmodcoordinatesat. fs_h_jt_smallmodcoordinatesat + S (jt_value_smallmodcoordinates) = S ((S (jt_index_smallmodcoordinates)) * c)) /\ exists fs_q_jt_smallmodcoordinatesat. b = fs_q_jt_smallmodcoordinatesat * S ((S (jt_index_smallmodcoordinates)) * c) + (jt_value_smallmodcoordinates))) -> (exists jt_factor_smallmodcoordinatesdivides. (jt_value_smallmodcoordinates)=(jt_divisor_smallmod)*jt_factor_smallmodcoordinatesdivides)) -> jt_divisor_smallmod=1)

Constructive proof overview

Generated structural guide

Primitivity descends from a modulus to a genuine divisor of it.

The unchanged tactic script uses 1 declared prerequisite 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

multiple_trans Alpha theorem; checked-use authorized

Direct dependents

JT000C jordan_primitive_tuple_product_components

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 · 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 assumptionsL1–10

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

  1. L1
    intro n
  2. L2
    intro m
  3. L3
    intro b
  4. L4
    intro c
  5. L5
    intro k
  6. L6
    intro hnm
  7. L7
    intro hp
  8. L8
    intro q
  9. L9
    intro hqn
  10. L10
    intro hall
02Use earlier factsL11–19

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

  1. L11
    specialize hp (q)
  2. L12
    apply hp
  3. L13
    specialize multiple_trans (n)
  4. L14
    specialize multiple_trans (q)
  5. L15
    specialize multiple_trans (m)
  6. L16
    apply multiple_trans
  7. L17
    exact hnm
  8. L18
    exact hqn
  9. L19
    exact hall

Library-wide reading audit

Original exact command ledger · 19 lines
  1. 0001intro n
  2. 0002intro m
  3. 0003intro b
  4. 0004intro c
  5. 0005intro k
  6. 0006intro hnm
  7. 0007intro hp
  8. 0008intro q
  9. 0009intro hqn
  10. 0010intro hall
  11. 0011specialize hp (q)
  12. 0012apply hp
  13. 0013specialize multiple_trans (n)
  14. 0014specialize multiple_trans (q)
  15. 0015specialize multiple_trans (m)
  16. 0016apply multiple_trans
  17. 0017exact hnm
  18. 0018exact hqn
  19. 0019exact hall