PD0012

Mod4Three(n)

n is three modulo four by an explicit quotient.

Conservative notation; not a theorem, primitive, or axiom.

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 h. n = 4 * h + 3

The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.

Direct definition dependencies

none — first-order arithmetic only

Definitions depending on this notation

PrimeThreeModFourDivisor(n,p)EuclidThreeNumber(c,n)

Checked theorems using this definition

TF0007 · three_mod_four_progression_nonzeroTF0008 · three_mod_four_progression_nonunitTF0009 · three_mod_four_progression_not_two_squareTF000A · three_mod_four_good_prime_exclusiveTF000D · three_mod_four_prime_divisor_existsTF0012 · infinitely_many_primes_three_mod_four