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.
Hygienic expanded first-order definition
exists ff_row_mdm_cell_research ff_column_mdm_cell_research. (((((exists ff_gap_mdm_lt_research_row_before. ff_gap_mdm_lt_research_row_before + S (i) = (r)) /\ ff_row_mdm_cell_research = i) \/ ((exists ff_gap_mdm_le_research_row_after. ff_gap_mdm_le_research_row_after + (r) = (i)) /\ ff_row_mdm_cell_research = S i))) /\ (((((exists ff_gap_mdm_lt_research_column_before. ff_gap_mdm_lt_research_column_before + S (j) = (d)) /\ ff_column_mdm_cell_research = j) \/ ((exists ff_gap_mdm_le_research_column_after. ff_gap_mdm_le_research_column_after + (d) = (j)) /\ ff_column_mdm_cell_research = S j))) /\ (((exists ff_h_mdm_research_source. ff_h_mdm_research_source + S (z) = S ((S ((ff_row_mdm_cell_research) * (w) + (ff_column_mdm_cell_research))) * c)) /\ exists ff_q_mdm_research_source. b = ff_q_mdm_research_source * S ((S ((ff_row_mdm_cell_research) * (w) + (ff_column_mdm_cell_research))) * c) + (z)))))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
Checked theorems using this definition
none directly; see definition consumers
Separate complete second-wave branches: Full T13 proof · Alpha v27.