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.
Statement with defined notation
∀ p. ∀ b. ∀ c. ∀ l. ¬p = 0 → ∃ x. ∃ y. ∃ z. ∃ n. DivisionPrefix(p,b,c,x,y,z,n,l)Every purple notation token opens its conservative definition. This reading surface never changes the unchanged intuitionistic kernel or confers checked-use authority.
Definitions used by this theorem
In the theorem statement
In local proof propositions
Exact expanded first-order statement
forall p b c l. ~(p = 0) -> exists qb qc db dc. (forall fdp_index_lucas_digits. (exists gsp_lt_gap_lucas_digits_index_bound. gsp_lt_gap_lucas_digits_index_bound + S fdp_index_lucas_digits = l) -> exists fdp_value_lucas_digits fdp_quotient_lucas_digits fdp_remainder_lucas_digits. (((exists ff_h_fdp_lucas_digits_source. ff_h_fdp_lucas_digits_source + S (fdp_value_lucas_digits) = S ((S (fdp_index_lucas_digits)) * c)) /\ exists ff_q_fdp_lucas_digits_source. b = ff_q_fdp_lucas_digits_source * S ((S (fdp_index_lucas_digits)) * c) + (fdp_value_lucas_digits))) /\ ((((exists ff_h_fdp_lucas_digits_quotient_entry. ff_h_fdp_lucas_digits_quotient_entry + S (fdp_quotient_lucas_digits) = S ((S (fdp_index_lucas_digits)) * qc)) /\ exists ff_q_fdp_lucas_digits_quotient_entry. qb = ff_q_fdp_lucas_digits_quotient_entry * S ((S (fdp_index_lucas_digits)) * qc) + (fdp_quotient_lucas_digits))) /\ ((((exists ff_h_fdp_lucas_digits_remainder_entry. ff_h_fdp_lucas_digits_remainder_entry + S (fdp_remainder_lucas_digits) = S ((S (fdp_index_lucas_digits)) * dc)) /\ exists ff_q_fdp_lucas_digits_remainder_entry. db = ff_q_fdp_lucas_digits_remainder_entry * S ((S (fdp_index_lucas_digits)) * dc) + (fdp_remainder_lucas_digits))) /\ (fdp_value_lucas_digits = p * fdp_quotient_lucas_digits + fdp_remainder_lucas_digits /\ (exists gsp_lt_gap_lucas_digits_remainder_bound. gsp_lt_gap_lucas_digits_remainder_bound + S fdp_remainder_lucas_digits = p)))))Proof neighborhood
Direct theorem prerequisites
Direct theorem dependents
Definition-aware tactic body
Only propositions whose conservative expansion has been checked for exact first-order equivalence are compacted. Every changed line retains its immutable exact replay command.
Read the argument
Proof checkpoints
This is a reading aid, not a new proof or a proof-tree certificate. Checkpoint groups are consecutive commands, not inferred branch boundaries. Every step links to the preserved script.
01Fix variables and assumptionsL1–5
02Use earlier factsL6–11
Instantiate or apply named facts and discharge the corresponding proof obligations.