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.
Statement with defined notation
∀ p. ∀ n. ∀ i. ∀ j. InverseIndex(p,n,i,j) → InverseIndex(p,n,j,i)Every purple notation token opens its conservative definition. This is a reading surface; the compiler expands the statement before the unchanged kernel checks it.
Definitions used by this theorem
In the theorem statement
2 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall p n i j. (((exists wip_strict_gap_symmetric_source_left_bound. wip_strict_gap_symmetric_source_left_bound + S i = n) /\ ((exists wip_strict_gap_symmetric_source_right_bound. wip_strict_gap_symmetric_source_right_bound + S j = n) /\ (exists wip_mod_left_symmetric_source_inverse wip_mod_right_symmetric_source_inverse. (S i) * S j + p * wip_mod_left_symmetric_source_inverse = 1 + p * wip_mod_right_symmetric_source_inverse)))) -> (((exists wip_strict_gap_symmetric_target_left_bound. wip_strict_gap_symmetric_target_left_bound + S j = n) /\ ((exists wip_strict_gap_symmetric_target_right_bound. wip_strict_gap_symmetric_target_right_bound + S i = n) /\ (exists wip_mod_left_symmetric_target_inverse wip_mod_right_symmetric_target_inverse. (S j) * S i + p * wip_mod_left_symmetric_target_inverse = 1 + p * wip_mod_right_symmetric_target_inverse))))Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only local propositions introduced by have or suffices are compacted. The untrusted compiler re-expands each one before the original tactic script is replayed; defined notation is never accepted by the kernel. Open the exact replay line beneath every changed command.
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.
Named ingredients (1)
01Fix variables and assumptionsL1–5
02Separate the logical casesL6–8
03Use earlier factsL9–9
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L9
exact hij_right_left
04Separate the logical casesL10–10
Follow the explicit conjunction, disjunction, witness, or contradiction step recorded below.
- L10
split
05Use earlier factsL11–11
Instantiate or apply named facts and discharge the corresponding proof obligations.
- L11
exact hij_left