PD0032

BoundedNonzeroInverse(m,a)

Public research checkpoint, not admitted to Alpha or Stable. Alpha v30 remains 3222 checked-use theorems; Stable remains 432. The on-demand Alpha Lean service does not yet expose these checkpoint theorems; their independently checked literal bundles and unchanged sources are available below.

a has a nonzero inverse strictly below m.

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

Definition in prerequisite notation

∃ dp_inverse. ¬dp_inverse = 0 ∧ (Lt(dp_inverse,m) ∧ BalancedInverse(m,a,dp_inverse))

Only definitions earlier in this acyclic notation graph are used here.

Hygienic expanded first-order definition 
exists dp_inverse. (~(dp_inverse = 0) /\ ((exists dp_bound. dp_bound + S dp_inverse = m) /\ (exists dp_u dp_v. (a) * (dp_inverse) + m * dp_u = 1 + m * dp_v)))

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

Direct definition dependencies

Lt(a,b)BalancedInverse(m,a,b)

Definitions depending on this notation

none

Checked theorems using this definition

FP001E · prime_field_inverse_exists