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.
Definition in prerequisite notation
∀ gcrt_positive_index_research. ∀ gcrt_positive_value_research. Lt(gcrt_positive_index_research,l) → Beta(b,c,gcrt_positive_index_research,gcrt_positive_value_research) → ¬gcrt_positive_value_research = 0Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall gcrt_positive_index_research gcrt_positive_value_research. (exists ff_lt_gcrt_research_bound. ff_lt_gcrt_research_bound + S gcrt_positive_index_research = l) -> (((exists ff_h_gcrt_research_entry. ff_h_gcrt_research_entry + S (gcrt_positive_value_research) = S ((S (gcrt_positive_index_research)) * c)) /\ exists ff_q_gcrt_research_entry. b = ff_q_gcrt_research_entry * S ((S (gcrt_positive_index_research)) * c) + (gcrt_positive_value_research))) -> ~(gcrt_positive_value_research = 0)The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.
Direct definition dependencies
Definitions depending on this notation
none