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
∃ ff_u_defined_sum. ∃ ff_v_defined_sum. BetaAt(ff_u_defined_sum,ff_v_defined_sum,0,0) ∧ (BetaAt(ff_u_defined_sum,ff_v_defined_sum,l,z) ∧ (∀ x. Lt(x,l) → ∃ y. ∃ n. ∃ m. BetaAt(b,c,x,y) ∧ (BetaAt(ff_u_defined_sum,ff_v_defined_sum,x,n) ∧ (BetaAt(ff_u_defined_sum,ff_v_defined_sum,S x,m) ∧ m = n + y))))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists ff_u_defined_sum ff_v_defined_sum. ((((exists ff_h_defined_sum_start. ff_h_defined_sum_start + S (0) = S ((S (0)) * ff_v_defined_sum)) /\ exists ff_q_defined_sum_start. ff_u_defined_sum = ff_q_defined_sum_start * S ((S (0)) * ff_v_defined_sum) + (0))) /\ ((((exists ff_h_defined_sum_terminal. ff_h_defined_sum_terminal + S (z) = S ((S (l)) * ff_v_defined_sum)) /\ exists ff_q_defined_sum_terminal. ff_u_defined_sum = ff_q_defined_sum_terminal * S ((S (l)) * ff_v_defined_sum) + (z))) /\ forall ff_i_defined_sum. (exists ff_lt_defined_sum_bound. ff_lt_defined_sum_bound + S ff_i_defined_sum = l) -> exists ff_a_defined_sum ff_r_defined_sum ff_s_defined_sum. ((((exists ff_h_defined_sum_summand. ff_h_defined_sum_summand + S (ff_a_defined_sum) = S ((S (ff_i_defined_sum)) * c)) /\ exists ff_q_defined_sum_summand. b = ff_q_defined_sum_summand * S ((S (ff_i_defined_sum)) * c) + (ff_a_defined_sum))) /\ ((((exists ff_h_defined_sum_partial. ff_h_defined_sum_partial + S (ff_r_defined_sum) = S ((S (ff_i_defined_sum)) * ff_v_defined_sum)) /\ exists ff_q_defined_sum_partial. ff_u_defined_sum = ff_q_defined_sum_partial * S ((S (ff_i_defined_sum)) * ff_v_defined_sum) + (ff_r_defined_sum))) /\ ((((exists ff_h_defined_sum_successor. ff_h_defined_sum_successor + S (ff_s_defined_sum) = S ((S (S ff_i_defined_sum)) * ff_v_defined_sum)) /\ exists ff_q_defined_sum_successor. ff_u_defined_sum = ff_q_defined_sum_successor * S ((S (S ff_i_defined_sum)) * ff_v_defined_sum) + (ff_s_defined_sum))) /\ ff_s_defined_sum = ff_r_defined_sum + ff_a_defined_sum)))))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.