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.
Definition in prerequisite notation
S a ≤ bOnly definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
exists h. h + S a = bThe 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
Checked theorems using this definition
BA000B · cf_approximation_first_recurrence_error_invariantBA000C · cf_approximation_prepend_recurrence_error_invariantBA001E · cf_approximation_small_positive_sum_current_zeroBA0021 · cf_approximation_small_denominator_signed_coordinatesBA0024 · cf_approximation_unimodular_best_approximationBA0025 · cf_approximation_alternating_identity_best_approximationBA0026 · cf_approximation_derived_invariant_best_signedBA002A · cf_convergent_old_history_successor_eliminationBA002B · cf_convergent_no_index_below_zeroBA002D · cf_convergent_old_history_nonempty_headBA0038 · cf_convergent_matrix_state_prefix_transportBA003A · cf_convergent_matrix_empty_existsBA003B · cf_convergent_matrix_extend_preserved_prefixBA003C · cf_convergent_matrix_prepend_existsBA003D · cf_convergent_euclidean_matrix_step_alignmentBA003E · cf_convergent_actual_prefix_error_invariantBA003F · cf_convergent_every_valid_matrix_prefix_existsBA0040 · cf_convergent_actual_prefix_index_boundBA0041 · continued_fraction_convergent_exists_at_history_indexBA0042 · continued_fraction_convergent_index_is_validBA0046 · continued_fraction_initial_zero_over_oneBA0047 · cf_convergent_full_matrix_is_exactBA004D · continued_fraction_convergent_exists_unique_at_history_index