let m, n be non empty Element of NAT ; :: thesis: for f being PartFunc of (REAL m),(REAL n)
for x being Element of REAL m st f is_differentiable_in x holds
diff f,x is LinearOperator of m,n
let f be PartFunc of (REAL m),(REAL n); :: thesis: for x being Element of REAL m st f is_differentiable_in x holds
diff f,x is LinearOperator of m,n
let x be Element of REAL m; :: thesis: ( f is_differentiable_in x implies diff f,x is LinearOperator of m,n )
assume f is_differentiable_in x ; :: thesis: diff f,x is LinearOperator of m,n
then diff f,x is LinearOperator of (REAL-NS m),(REAL-NS n) by LMBOP2;
hence diff f,x is LinearOperator of m,n by EQLOPBDef56; :: thesis: verum