:: deftheorem Def7 defines `| FDIFF_1:def 7 :
for f being PartFunc of REAL,REAL
for X being set st f is_differentiable_on X holds
for b<sub>3</sub> being PartFunc of REAL,REAL holds
( b<sub>3</sub> = f `| X iff ( dom b₃ = X & ( for x being Real st x in X holds
b₃ . x = diff (f,x) ) ) );