Current library: Alpha v34, 4,223 checked-use theorems; Stable remains 432. Historical first admissions, original proof editions, and non-admitted aliases are preserved.
Definition in prerequisite notation
z = ((up + us) · S (up + us) + (us + us) + ((un + ut) · S (un + ut) + (ut + ut))) · S ((up + us) · S (up + us) + (us + us) + ((un + ut) · S (un + ut) + (ut + ut))) + ((un + ut) · S (un + ut) + (ut + ut) + ((un + ut) · S (un + ut) + (ut + ut)))Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
z = ((((up) + (us)) * S ((up) + (us)) + ((us) + (us))) + (((un) + (ut)) * S ((un) + (ut)) + ((ut) + (ut)))) * S ((((up) + (us)) * S ((up) + (us)) + ((us) + (us))) + (((un) + (ut)) * S ((un) + (ut)) + ((ut) + (ut)))) + ((((un) + (ut)) * S ((un) + (ut)) + ((ut) + (ut))) + (((un) + (ut)) * S ((un) + (ut)) + ((ut) + (ut))))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