Record C1_fun : Type := mkC1
  {c1 :> R -> R; diff0 : derivable c1; cont1 : continuity (derive c1 diff0)}.Record C1_fun : Type := mkC1
  {c1 :> R -> R; diff0 : derivable c1; cont1 : continuity (derive c1 diff0)}.Record C1_fun : Type := mkC1
  {c1 :> R -> R; diff0 : derivable c1; cont1 : continuity (derive c1 diff0)}.Record C1_fun : Type := mkC1
  {c1 :> R -> R; diff0 : derivable c1; cont1 : continuity (derive c1 diff0)}.Record C1_fun : Type := mkC1
  {c1 :> R -> R; diff0 : derivable c1; cont1 : continuity (derive c1 diff0)}.

Lemma RiemannInt_P31 : forall (f:C1_fun) (a b:R), a <= b -> antiderivative (derive f (diff0 f)) f a b.