fact: Definition StepApproxDiscretize {IS : IntegrationSpace} (f : PartialFunction (X (ElemFunc IS))) (fInt : IntegrableFunction f) (a b eta : CRcarrier (RealT (ElemFunc IS))) (aPos : 0 < a) (ltab : a < b) (aeta : 0 < a - eta < a) (beta : 0 < b < b + eta) (n i : nat) : CRcarrier (RealT (ElemFunc IS)) := match i with | O => Integral (StepApproxIntegrable f (a - eta) a aeta fInt) | S j => if le_lt_dec (S (2 ^ n)) i then Integral (StepApproxIntegrable f b (b + eta) beta fInt) else Integral (StepApproxIntegrable f (BinarySubdiv a b n j) (BinarySubdiv a b n (S j)) (BinarySubdivIncr a b n j (pair aPos ltab)) fInt) end.
imports: QArith_base Qabs ConstructiveReals ConstructiveSum ConstructivePower ConstructiveAbs ConstructiveMinMax ConstructiveLimits ConstructiveUniformCont ConstructivePartialFunctions ConstructiveDiagonal CMTbase CMTIntegrableFunctions CMTIntegrableSets CMTFullSets CMTReals Lia