ND0070 · conservative definition

EuclidParameters

Explicit m>n>0, coprime opposite-parity parameters, c=m²+n², the subtraction-free odd-leg equation m²=n²+a, and b=2mn.

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

EuclidParameters(a, b, c, m, n)

Exact expansion

(~((n) = 0) /\ ((exists pi_gap_firstwave. pi_gap_firstwave + S (n) = (m)) /\ ((forall pff_divisor_pi_firstwave_coprime. (exists pff_left_pi_firstwave_coprime. (m) = pff_divisor_pi_firstwave_coprime * pff_left_pi_firstwave_coprime) -> (exists pff_right_pi_firstwave_coprime. (n) = pff_divisor_pi_firstwave_coprime * pff_right_pi_firstwave_coprime) -> pff_divisor_pi_firstwave_coprime = 1) /\ (((((exists pp_even_pi_firstwave_parity_first_even. (m) = 2 * pp_even_pi_firstwave_parity_first_even) /\ (exists pp_odd_pi_firstwave_parity_second_odd. (n) = 2 * pp_odd_pi_firstwave_parity_second_odd + 1)) \/ ((exists pp_odd_pi_firstwave_parity_first_odd. (m) = 2 * pp_odd_pi_firstwave_parity_first_odd + 1) /\ (exists pp_even_pi_firstwave_parity_second_even. (n) = 2 * pp_even_pi_firstwave_parity_second_even)))) /\ ((c) = (m) * (m) + (n) * (n) /\ ((m) * (m) = (n) * (n) + (a) /\ (b) = 2 * ((m) * (n))))))))

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

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Used by theorem statements or local proof propositions

Grand-campaign planning vocabulary

Locate EuclidParameters in the global campaign vocabulary →

Reviewed EuclidParameters corresponds to blueprint EuclidParameters with checked argument positions [0, 1, 2, 3, 4].

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.