let X be set ; :: thesis: for f being PartFunc of REAL ,REAL st f is_differentiable_on X holds
X is Subset of REAL
let f be PartFunc of REAL ,REAL ; :: thesis: ( f is_differentiable_on X implies X is Subset of REAL )
assume f is_differentiable_on X ; :: thesis: X is Subset of REAL
then X c= dom f by Def7;
hence X is Subset of REAL by XBOOLE_1:1; :: thesis: verum