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
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All transitive conservative prerequisites
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Used by theorem statements or local proof propositions
SL0003 quadratic_supplement_minus_one_half_parity SL0004 quadratic_supplement_minus_one_residue_iff_mod_four_one SL0005 quadratic_supplement_minus_one_nonresidue_iff_mod_four_three SL0006 quadratic_supplement_minus_one_complete SL0007 bounded_gauss_lemma_complete SL0009 odd_mod_eight_cases SL000D doubling_gauss_even_count_implies_good_mod_eight SL000E doubling_gauss_odd_count_implies_bad_mod_eight SL000F doubling_gauss_count_parity_mod_eight_complete SL000O quadratic_supplement_two_conditional_on_gauss_count_shape SL000Q quadratic_supplement_two_half_complete SL000R quadratic_supplement_two_residue_iff_mod_eight_one_or_seven SL000S quadratic_supplement_two_nonresidue_iff_mod_eight_three_or_five SL000T quadratic_supplement_two_completeGrand-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.