reserve n for Nat,
        p,p1,p2 for Point of TOP-REAL n,
        x for Real;
reserve n,m for non zero Nat;
reserve i,j for Nat;
reserve f for PartFunc of REAL-NS m,REAL-NS n;
reserve g for PartFunc of REAL m,REAL n;
reserve h for PartFunc of REAL m,REAL;
reserve x for Point of REAL-NS m;
reserve y for Element of REAL m;
reserve X for set;

theorem Th17:
for x be Element of REAL,i be Nat st
  1 <=i & i <= m & x <> 0 holds reproj(i,0*m).x <> 0*m
proof
   let x be Element of REAL, i be Nat;
   assume 1 <=i & i <= m & x <> 0;
   then Replace(0*m,i,x) <> 0*m by Th11;
   hence thesis by PDIFF_1:def 5;
end;
