let i be Element of NAT ; :: thesis: for X being set
for m, n being non empty Element of NAT
for f being PartFunc of (REAL m),(REAL n) st f is_partial_differentiable_on X,i holds
X is Subset of (REAL m)
let X be set ; :: thesis: for m, n being non empty Element of NAT
for f being PartFunc of (REAL m),(REAL n) st f is_partial_differentiable_on X,i holds
X is Subset of (REAL m)
let m, n be non empty Element of NAT ; :: thesis: for f being PartFunc of (REAL m),(REAL n) st f is_partial_differentiable_on X,i holds
X is Subset of (REAL m)
let f be PartFunc of (REAL m),(REAL n); :: thesis: ( f is_partial_differentiable_on X,i implies X is Subset of (REAL m) )
assume f is_partial_differentiable_on X,i ; :: thesis: X is Subset of (REAL m)
then X c= dom f by Def4;
hence X is Subset of (REAL m) by XBOOLE_1:1; :: thesis: verum