PD0019

Repeat(b,c,a,l)

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.

The decoded prefix repeats a for l positions.

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

Definition in prerequisite notation

∀ ff_i_defined_repeat. Lt(ff_i_defined_repeat,l) → BetaAt(b,c,ff_i_defined_repeat,a)

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

Hygienic expanded first-order definition 
forall ff_i_defined_repeat. (exists ff_lt_defined_repeat_bound. ff_lt_defined_repeat_bound + S ff_i_defined_repeat = l) -> (((exists ff_h_defined_repeat_decoded. ff_h_defined_repeat_decoded + S (a) = S ((S (ff_i_defined_repeat)) * c)) /\ exists ff_q_defined_repeat_decoded. b = ff_q_defined_repeat_decoded * S ((S (ff_i_defined_repeat)) * c) + (a)))

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)BetaAt(b,c,i,x)

Definitions depending on this notation

none

Checked theorems using this definition

PP0009 · prime_field_polynomial_repeat_coefficientsPP000A · prime_field_polynomial_repeat_existsPP000B · prime_field_polynomial_zero_existsPP0013 · prime_field_polynomial_add_zero_rightPP0014 · prime_field_polynomial_scale_from_normalizationPP0015 · prime_field_polynomial_scale_existsPP001B · prime_field_polynomial_scale_zeroPP002E · prime_field_polynomial_horner_zero