reserve f for PartFunc of REAL-NS 1,REAL-NS 1;
reserve g for PartFunc of REAL,REAL;
reserve x for Point of REAL-NS 1;
reserve y for Real;
reserve m,n for non zero Nat;
reserve i,j for Nat;
reserve f for PartFunc of REAL-NS n,REAL-NS 1;
reserve g for PartFunc of REAL n,REAL;
reserve x for Point of REAL-NS n;
reserve y for Element of REAL n;
reserve X for set;
reserve r for Real;
reserve f,f1,f2 for PartFunc of REAL-NS m,REAL-NS n;
reserve g,g1,g2 for PartFunc of REAL n,REAL;
reserve h for PartFunc of REAL m,REAL n;
reserve x for Point of REAL-NS m;
reserve y for Element of REAL n;
reserve z for Element of REAL m;

theorem Th25:
  f is_partial_differentiable_on X,i implies X is Subset of REAL-NS m
by XBOOLE_1:1;
