FS0027

four_square_euler_mixed_ac

Dependency-curried candidate body; not Alpha-enrolled; no checked-use authority

The two mixed Hamilton products for the ac left-coordinate pair cancel exactly.

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 a b c d e f g h. ((((a * f) * (c * h) = (a * h) * (c * f))) /\ (((a * g) * (c * e) = (a * e) * (c * g))))

Constructive proof overview

Generated structural guide

The two mixed Hamilton products for the ac left-coordinate pair cancel exactly.

The unchanged tactic script uses 1 declared prerequisite and contains 19 exact native proof lines.

dependency-curried kernel-checked theorem body; Alpha enrollment and checked-use authority follow separately sealed release evidence; Stable membership remains unchanged

Proof neighborhood

Direct dependencies

FS0025 four_square_euler_cross_swap

Direct dependents

FS002C four_square_euler_all_mixed_cancel

Formal native tactic body

Dependencies are introduced as named hypotheses before line 1. Local theorem links identify exact declared prerequisites. This dependency-curried candidate body does not grant checked theorem use or 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.

Named ingredients (1)
four square euler cross swap
01Fix variables and assumptionsL1–8

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

  1. L1
    intro a
  2. L2
    intro b
  3. L3
    intro c
  4. L4
    intro d
  5. L5
    intro e
  6. L6
    intro f
  7. L7
    intro g
  8. L8
    intro h
02Separate the logical casesL9–9

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

  1. L9
    split
03Use earlier factsL10–19

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

  1. L10
    specialize four_square_euler_cross_swap a
  2. L11
    specialize four_square_euler_cross_swap f
  3. L12
    specialize four_square_euler_cross_swap c
  4. L13
    specialize four_square_euler_cross_swap h
  5. L14
    exact four_square_euler_cross_swap
  6. L15
    specialize four_square_euler_cross_swap a
  7. L16
    specialize four_square_euler_cross_swap g
  8. L17
    specialize four_square_euler_cross_swap c
  9. L18
    specialize four_square_euler_cross_swap e
  10. L19
    exact four_square_euler_cross_swap

Library-wide reading audit

Original exact command ledger · 19 lines
  1. 0001intro a
  2. 0002intro b
  3. 0003intro c
  4. 0004intro d
  5. 0005intro e
  6. 0006intro f
  7. 0007intro g
  8. 0008intro h
  9. 0009split
  10. 0010specialize four_square_euler_cross_swap a
  11. 0011specialize four_square_euler_cross_swap f
  12. 0012specialize four_square_euler_cross_swap c
  13. 0013specialize four_square_euler_cross_swap h
  14. 0014exact four_square_euler_cross_swap
  15. 0015specialize four_square_euler_cross_swap a
  16. 0016specialize four_square_euler_cross_swap g
  17. 0017specialize four_square_euler_cross_swap c
  18. 0018specialize four_square_euler_cross_swap e
  19. 0019exact four_square_euler_cross_swap