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
Odd(n)Exact expansion
exists h. n = 2 * h + 1This 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
none
Used by conservative definitions
All transitive conservative prerequisites
none
Used by theorem statements or local proof propositions
PF000I pythagorean_parameter_odd_square PF000J pythagorean_even_odd_square_gap_odd PF000K pythagorean_odd_even_square_gap_odd PF000L pythagorean_opposite_parity_square_gap_odd PF000M pythagorean_opposite_parity_hypotenuse_odd PF000N pythagorean_odd_coordinate_coprime_two PF000S pythagorean_primitive_euclidean_legs PF0010 pythagorean_odd_square_pair_two_mod_four PF0012 pythagorean_triple_legs_not_both_odd PF0013 pythagorean_coordinate_parity_choice PF0014 pythagorean_primitive_legs_opposite_parity PF0015 pythagorean_odd_square_has_odd_root PF0016 pythagorean_primitive_hypotenuse_odd PF0017 pythagorean_primitive_normal_form PF001J pythagorean_odd_ordered_difference_even PF001P pythagorean_even_square_has_even_root PF001Q pythagorean_odd_square_sum_opposite_roots PF001V pythagorean_odd_even_half_factors PF001W pythagorean_half_factors_extract_parameters PF001X pythagorean_primitive_odd_even_inverse PF002C fermat_four_even_square_root PF002E fermat_four_odd_double_square_factors PF002K fermat_four_primitive_odd_even_descentGrand-campaign planning vocabulary
Locate Odd in the global campaign vocabulary →
Reviewed Odd corresponds to blueprint Odd with checked argument positions [0].
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.