proposition: Lemma lipschitz_set1 (K : numFieldType) (V W : normedModType K) (f : V -> W) (a : V) : [lipschitz f x | x in [set a]].
proof: Proof. apply: (@klipschitzW _ _ _ `|f a|). exact: (@globally_properfilter _ _ (a, a)). by move=> [x y] /= [] -> ->; rewrite !subrr !normr0 mulr0. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule