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
∀ b. ∀ c. ∀ m. ∃ x. ∃ y. ∀ z. ∀ n. Lt(z,m + m) → BetaAt(b,c,z,n) → BetaAt(x,y,z,S n)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
3 occurrences
In local proof propositions
0 occurrences
Exact expanded native-PA statement
forall b c m. (exists f g. (forall wsl_index_wsl_lift wsl_value_wsl_lift. (exists wpo_gap_wsl_lift_bound. wpo_gap_wsl_lift_bound + S (wsl_index_wsl_lift) = m + m) -> (((exists wpo_beta_height_wsl_lift_source. wpo_beta_height_wsl_lift_source + S (wsl_value_wsl_lift) = S ((S (wsl_index_wsl_lift)) * c)) /\ exists wpo_beta_quotient_wsl_lift_source. b = wpo_beta_quotient_wsl_lift_source * S ((S (wsl_index_wsl_lift)) * c) + (wsl_value_wsl_lift))) -> (((exists wpo_beta_height_wsl_lift_target. wpo_beta_height_wsl_lift_target + S (S wsl_value_wsl_lift) = S ((S (wsl_index_wsl_lift)) * g)) /\ exists wpo_beta_quotient_wsl_lift_target. f = wpo_beta_quotient_wsl_lift_target * S ((S (wsl_index_wsl_lift)) * g) + (S wsl_value_wsl_lift)))))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.