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 s u U v V l r m z. l = ((u) + (U)) * S ((u) + (U)) + ((U) + (U)) -> r = ((v) + (V)) * S ((v) + (V)) + ((V) + (V)) -> m = ((l) + (r)) * S ((l) + (r)) + ((r) + (r)) -> z = ((s) + (m)) * S ((s) + (m)) + ((m) + (m)) -> (exists cfc_left_state_constructor cfc_right_state_constructor cfc_matrix_state_constructor. ((cfc_left_state_constructor = ((u) + (U)) * S ((u) + (U)) + ((U) + (U))) /\ ((cfc_right_state_constructor = ((v) + (V)) * S ((v) + (V)) + ((V) + (V))) /\ ((cfc_matrix_state_constructor = ((cfc_left_state_constructor) + (cfc_right_state_constructor)) * S ((cfc_left_state_constructor) + (cfc_right_state_constructor)) + ((cfc_right_state_constructor) + (cfc_right_state_constructor))) /\ ((z) = ((s) + (cfc_matrix_state_constructor)) * S ((s) + (cfc_matrix_state_constructor)) + ((cfc_matrix_state_constructor) + (cfc_matrix_state_constructor)))))))Constructive proof overview
Generated structural guide
Conservative existential sharing constructs the exact five-coordinate state without adding a pairing function to HA.
The unchanged tactic script uses 0 declared prerequisites and contains 23 exact native proof lines.
Alpha v34 checked-use · first admitted v29 · independently kernel and Lean verified; not Stable
Proof neighborhood
Direct dependencies
Direct dependents
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
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
02Fix variables and assumptionsL11–13
03Construct an explicit witnessL14–16
04Separate the logical casesL17–17
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L17
split
05Use earlier factsL18–18
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L18
exact hl
06Separate the logical casesL19–19
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L19
split
07Use earlier factsL20–20
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L20
exact hr
08Separate the logical casesL21–21
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L21
split