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.
Readable signature
OppositeParity(m, n)Exact expansion
(((exists pp_even_frontier_first_even. (m) = 2 * pp_even_frontier_first_even) /\ (exists pp_odd_frontier_second_odd. (n) = 2 * pp_odd_frontier_second_odd + 1)) \/ ((exists pp_odd_frontier_first_odd. (m) = 2 * pp_odd_frontier_first_odd + 1) /\ (exists pp_even_frontier_second_even. (n) = 2 * pp_even_frontier_second_even)))This node is conservative notation, not a theorem, axiom, predicate constant, or kernel rule. Its expansion remains in the unchanged first-order language.
Definition neighborhood
Depends on conservative definitions
Used by conservative definitions
All transitive conservative prerequisites
Used by theorem statements or local proof propositions
PF000L pythagorean_opposite_parity_square_gap_odd PF000M pythagorean_opposite_parity_hypotenuse_odd PF000S pythagorean_primitive_euclidean_legs PF000T pythagorean_primitive_euclidean_constructor PF000U pythagorean_primitive_euclidean_from_order PF000V pythagorean_primitive_euclidean_swapped_constructor PF0014 pythagorean_primitive_legs_opposite_parity PF0016 pythagorean_primitive_hypotenuse_odd PF0017 pythagorean_primitive_normal_form PF001J pythagorean_odd_ordered_difference_even PF001Q pythagorean_odd_square_sum_opposite_roots PF001Z pythagorean_positive_primitive_inverse PF0022 pythagorean_positive_primitive_from_parameters PF002L fermat_four_primitive_descentGrand-campaign planning vocabulary
Locate OppositeParity in the global campaign vocabulary →
Reviewed OppositeParity corresponds to blueprint OppositeParity with checked argument positions [0, 1].
The global atlas describes planning vocabulary and does not itself certify a definition or theorem. The reviewed expansion and conservative dependency DAG on this page are the actual family-local reading definitions.