reserve n,k for Element of NAT;
reserve x,y,X for set;
reserve g,r,p for Real;
reserve S for RealNormSpace;
reserve rseq for Real_Sequence;
reserve seq,seq1 for sequence of S;
reserve x0 for Point of S;
reserve Y for Subset of S;
reserve S,T for RealNormSpace;
reserve f,f1,f2 for PartFunc of S,T;
reserve s1 for sequence of S;
reserve x0 for Point of S;
reserve h for (0.S)-convergent sequence of S;
reserve c for constant sequence of S;
reserve R,R1,R2 for RestFunc of S,T;
reserve L,L1,L2 for Point of R_NormSpace_of_BoundedLinearOperators(S,T);

theorem Th26:
  for h be PartFunc of S,T for seq be sequence of S for r be Real
  holds h is total implies (r(#)h)/*seq = r*(h/*seq)
proof
  let h be PartFunc of S,T;
  let seq be sequence of S;
  let r be Real;
  assume h is total;
  then dom h = the carrier of S by PARTFUN1:def 2;
  then rng seq c= dom h;
  hence thesis by NFCONT_1:13;
end;
