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
∀ cfc_numerator_prioritylayer. ∀ cfc_negative_numerator_prioritylayer. ∀ cfc_denominator_prioritylayer. ∀ cfc_current_error_prioritylayer. ∀ cfc_candidate_error_prioritylayer. ¬cfc_denominator_prioritylayer = 0 → Lt(cfc_denominator_prioritylayer,v) → NaturalAbsDifference(a · v,b · u,cfc_current_error_prioritylayer) → NaturalAbsDifference(a · cfc_denominator_prioritylayer + b · cfc_negative_numerator_prioritylayer,b · cfc_numerator_prioritylayer,cfc_candidate_error_prioritylayer) → Le(cfc_current_error_prioritylayer,cfc_candidate_error_prioritylayer)Only definitions earlier in this acyclic notation graph are used here.
Hygienic expanded first-order definition
forall cfc_numerator_prioritylayer cfc_negative_numerator_prioritylayer cfc_denominator_prioritylayer cfc_current_error_prioritylayer cfc_candidate_error_prioritylayer. ~(cfc_denominator_prioritylayer = 0) -> (exists cfba_gap_prioritylayerdenominator. cfba_gap_prioritylayerdenominator + S (cfc_denominator_prioritylayer) = (v)) -> ((((a) * (v)) = ((b) * (u)) + (cfc_current_error_prioritylayer)) \/ (((b) * (u)) = ((a) * (v)) + (cfc_current_error_prioritylayer))) -> ((((a) * cfc_denominator_prioritylayer + (b) * cfc_negative_numerator_prioritylayer) = ((b) * cfc_numerator_prioritylayer) + (cfc_candidate_error_prioritylayer)) \/ (((b) * cfc_numerator_prioritylayer) = ((a) * cfc_denominator_prioritylayer + (b) * cfc_negative_numerator_prioritylayer) + (cfc_candidate_error_prioritylayer))) -> (exists cfba_bound_prioritylayerresult. cfba_bound_prioritylayerresult + (cfc_current_error_prioritylayer) = (cfc_candidate_error_prioritylayer))The unchanged native kernel never receives this surface symbol. Binder-safe expansion produces only its existing first-order syntax.
Direct definition dependencies
Definitions depending on this notation
none