JT0037

jordan_rectangle_pair_unique

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

Actual bounded quotient/remainder decomposition uniquely recovers both indices.

Exact expanded first-order arithmetic statement

forall v i j r s. (exists jt_gap_uniquecolumn. jt_gap_uniquecolumn+S (j)=(v)) -> (exists jt_gap_uniqueother. jt_gap_uniqueother+S (s)=(v)) -> v*i+j=v*r+s -> (i=r /\ j=s)

Constructive proof overview

Generated structural guide

Actual bounded quotient/remainder decomposition uniquely recovers both indices.

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

division_remainder_unique Alpha theorem; checked-use authorized

Direct dependents

JT0044 jordan_rectangle_crt_pair_value

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 · 4 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 v
  2. L2
    intro i
  3. L3
    intro j
  4. L4
    intro r
  5. L5
    intro s
  6. L6
    intro hj
  7. L7
    intro hs
  8. L8
    intro heq
02Use earlier factsL9–15

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

  1. L9
    specialize division_remainder_unique (v)
  2. L10
    specialize division_remainder_unique (v*i+j)
  3. L11
    specialize division_remainder_unique (i)
  4. L12
    specialize division_remainder_unique (j)
  5. L13
    specialize division_remainder_unique (r)
  6. L14
    specialize division_remainder_unique (s)
  7. L15
    apply division_remainder_unique
03Calculate and transport equalitiesL16–16

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

  1. L16
    refl
04Use earlier factsL17–19

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

  1. L17
    exact hj
  2. L18
    exact heq
  3. L19
    exact hs

Library-wide reading audit

Original exact command ledger · 19 lines
  1. 0001intro v
  2. 0002intro i
  3. 0003intro j
  4. 0004intro r
  5. 0005intro s
  6. 0006intro hj
  7. 0007intro hs
  8. 0008intro heq
  9. 0009specialize division_remainder_unique (v)
  10. 0010specialize division_remainder_unique (v*i+j)
  11. 0011specialize division_remainder_unique (i)
  12. 0012specialize division_remainder_unique (j)
  13. 0013specialize division_remainder_unique (r)
  14. 0014specialize division_remainder_unique (s)
  15. 0015apply division_remainder_unique
  16. 0016refl
  17. 0017exact hj
  18. 0018exact heq
  19. 0019exact hs