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
∀ ics_index_secondwave. ∀ ics_value0_secondwave. ∀ ics_value1_secondwave. ∀ ics_value2_secondwave. ∀ ics_value3_secondwave. ∀ ics_value4_secondwave. ∀ ics_value5_secondwave. Lt(ics_index_secondwave,l) → BetaAt(ab,ac,ics_index_secondwave,ics_value0_secondwave) → BetaAt(db,dc,ics_index_secondwave,ics_value1_secondwave) → BetaAt(eb,ec,ics_index_secondwave,ics_value2_secondwave) → BetaAt(fb,fc,ics_index_secondwave,ics_value3_secondwave) → BetaAt(pb,pc,ics_index_secondwave,ics_value4_secondwave) → BetaAt(nb,nc,ics_index_secondwave,ics_value5_secondwave) → ics_value4_secondwave + (ics_value1_secondwave + ics_value3_secondwave) = ics_value0_secondwave + ics_value2_secondwave + ics_value5_secondwaveOnly definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall ics_index_secondwave ics_value0_secondwave ics_value1_secondwave ics_value2_secondwave ics_value3_secondwave ics_value4_secondwave ics_value5_secondwave. (exists ics_gap_secondwave_bound. ics_gap_secondwave_bound + S (ics_index_secondwave) = (l)) -> (((exists fs_h_ics_secondwave_at0. fs_h_ics_secondwave_at0 + S (ics_value0_secondwave) = S ((S (ics_index_secondwave)) * ac)) /\ exists fs_q_ics_secondwave_at0. ab = fs_q_ics_secondwave_at0 * S ((S (ics_index_secondwave)) * ac) + (ics_value0_secondwave))) -> (((exists fs_h_ics_secondwave_at1. fs_h_ics_secondwave_at1 + S (ics_value1_secondwave) = S ((S (ics_index_secondwave)) * dc)) /\ exists fs_q_ics_secondwave_at1. db = fs_q_ics_secondwave_at1 * S ((S (ics_index_secondwave)) * dc) + (ics_value1_secondwave))) -> (((exists fs_h_ics_secondwave_at2. fs_h_ics_secondwave_at2 + S (ics_value2_secondwave) = S ((S (ics_index_secondwave)) * ec)) /\ exists fs_q_ics_secondwave_at2. eb = fs_q_ics_secondwave_at2 * S ((S (ics_index_secondwave)) * ec) + (ics_value2_secondwave))) -> (((exists fs_h_ics_secondwave_at3. fs_h_ics_secondwave_at3 + S (ics_value3_secondwave) = S ((S (ics_index_secondwave)) * fc)) /\ exists fs_q_ics_secondwave_at3. fb = fs_q_ics_secondwave_at3 * S ((S (ics_index_secondwave)) * fc) + (ics_value3_secondwave))) -> (((exists fs_h_ics_secondwave_at4. fs_h_ics_secondwave_at4 + S (ics_value4_secondwave) = S ((S (ics_index_secondwave)) * pc)) /\ exists fs_q_ics_secondwave_at4. pb = fs_q_ics_secondwave_at4 * S ((S (ics_index_secondwave)) * pc) + (ics_value4_secondwave))) -> (((exists fs_h_ics_secondwave_at5. fs_h_ics_secondwave_at5 + S (ics_value5_secondwave) = S ((S (ics_index_secondwave)) * nc)) /\ exists fs_q_ics_secondwave_at5. nb = fs_q_ics_secondwave_at5 * S ((S (ics_index_secondwave)) * nc) + (ics_value5_secondwave))) -> ics_value4_secondwave + (ics_value1_secondwave + ics_value3_secondwave) = (ics_value0_secondwave + ics_value2_secondwave) + ics_value5_secondwaveThe 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
Checked theorems using this definition
DL0073 · integer_vector_add_from_component_sumsDL0074 · integer_vector_add_existsDL0075 · integer_vector_add_transport_inputsDL0076 · integer_vector_add_functionalDL007B · integer_matrix_vector_add_coefficientsDL007C · integer_matrix_vector_add_constructiveDL0082 · integer_column_span_add_closedDL0083 · integer_column_span_add_exists