proposition: Theorem seq_lim_cont `{ExtMetricSpaceClass X, ExtMetricSpaceClass Y} (f : X -> Y) {mu : Q -> Qinf} {_ : IsUniformlyContinuous f mu} (x : seq X) (a : X) (N : Q -> nat) : seq_lim x a N → seq_lim (f ∘ x) (f a) (comp_inf N mu 0).
proof: Proof. intros A e e_pos n A1. apply (uc_prf f mu); trivial. unfold comp_inf in A1; assert (A2 := uc_pos f mu e e_pos). now destruct (mu e); [apply A | apply mspc_inf]. Qed.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity Coq.QArith.QArith MathClasses.theory.setoids MathClasses.theory.products MathClasses.implementations.stdlib_rationals MathClasses.interfaces.abstract_algebra MathClasses.implementations.QType_rationals MathClasses.interfaces.additional_operations CoRN.tactics.Qauto Coq.QArith.QOrderedType MathClasses.theory.rings MathClasses.theory.dec_fields MathClasses.orders.rings MathClasses.orders.dec_fields MathClasses.theory.nat_pow MathClasses.interfaces.naturals MathClasses.interfaces.orders CoRN.reals.fast.CRGeometricSum