fact: Definition picard' (f : sx -> sy) `{!@IsUniformlyContinuous sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sy (@sig_mspc_ball CR (msp_mspc_ball CR) (ball (proj1_sig ry) y0)) f mu_f} : Q -> CR := λ x, y0 + @int (extend x0 rx (v ∘ (together Datatypes.id f) ∘ diag)) (@Integral_instance_0 (extend x0 rx (v ∘ (together Datatypes.id f) ∘ diag)) _ (@uc_ulc Q (msp_mspc_ball Q_as_MetricSpace) CR (msp_mspc_ball CR) (extend x0 rx (v ∘ (together Datatypes.id f) ∘ diag)) _ (@extend_uc CR (msp_mspc_ball CR) (msp_mspc_ball_ext CR) x0 rx _ _ (@compose_uc sx (sx and sx) CR (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@Linf_product_metric_space_ball sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0))) (@Linf_product_metric_space_class sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0))) (msp_mspc_ball CR) (@diag sx) (v ∘ @together sx sx sx sy (@Datatypes.id sx) f) (lip_modulus 1) (@comp_inf Q Qinf (λ e : Q, @minmax.min Qinf Qinf_le metric.Decision_instance_0 (lip_modulus 1 e) (mu_f e)) mu_v Qinf.infinite) (@lip_uc sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (sx and sx) (@Linf_product_metric_space_ball sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0))) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_msd Q (ball (proj1_sig rx) x0) Qmsd) (@sig_mspc_distance Q_as_MetricSpace (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0) Qmsd Qmsc) (@Linf_product_metric_space_class sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0))) (@diag sx) 1 (@diag_lip sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)))) (@compose_uc (sx and sx) (sx and sy) CR (@Linf_product_metric_space_ball sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0))) (@Linf_product_metric_space_ball sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sy (@sig_mspc_ball CR (msp_mspc_ball CR) (ball (proj1_sig ry) y0))) (@Linf_product_metric_space_class sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sy (@sig_mspc_ball CR (msp_mspc_ball CR) (ball (proj1_sig ry) y0)) (@sig_mspc CR (msp_mspc_ball CR) (msp_mspc_ball_ext CR) (ball (proj1_sig ry) y0))) (msp_mspc_ball CR) (@together sx sx sx sy (@Datatypes.id sx) f) v (λ e : Q, @minmax.min Qinf Qinf_le metric.Decision_instance_0 (lip_modulus 1 e) (mu_f e)) mu_v (@together_uc sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sy (@sig_mspc_ball CR (msp_mspc_ball CR) (ball (proj1_sig ry) y0)) (@sig_mspc CR (msp_mspc_ball CR) (msp_mspc_ball_ext CR) (ball (proj1_sig ry) y0)) (@Datatypes.id sx) f (lip_modulus 1) (@lip_uc sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_msd Q (ball (proj1_sig rx) x0) Qmsd) (@sig_mspc_distance Q_as_MetricSpace (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0) Qmsd Qmsc) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@Datatypes.id sx) 1 (@id_lip sx (@sig_mspc_ball Q (msp_mspc_ball Q_as_MetricSpace) (ball (proj1_sig rx) x0)) (@sig_mspc Q (msp_mspc_ball Q_as_MetricSpace) (msp_mspc_ball_ext Q_as_MetricSpace) (ball (proj1_sig rx) x0)))) mu_f _) _))))) x0 x.
imports: CoRN.algebra.RSetoid CoRN.metric2.Metric CoRN.metric2.UniformContinuity CoRN.model.reals.CRreal Coq.Unicode.Utf8 Coq.Program.Program CoRN.reals.fast.CRArith CoRN.reals.fast.CRabs CoRN.tactics.Qauto Coq.QArith.Qround CoRN.model.metric2.Qmetric  CoRN.ode.metric CoRN.ode.FromMetric2 CoRN.ode.AbstractIntegration CoRN.ode.SimpleIntegration CoRN.ode.BanachFixpoint MathClasses.interfaces.canonical_names MathClasses.misc.decision MathClasses.misc.setoid_tactics MathClasses.misc.util MathClasses.implementations.stdlib_rationals MathClasses.theory.rationals