reserve m,n for non zero Element of NAT;
reserve i,j,k for Element of NAT;
reserve Z for set;

theorem Th6:
for f be PartFunc of REAL i,REAL, x be Element of REAL i st
  x in dom f holds (<>*f).x = <* f.x *> & (<>*f)/.x = <* f/.x *>
proof
   let f be PartFunc of REAL i,REAL, x be Element of REAL i;
   set I=proj(1,1) qua Function";
   assume A1: x in dom f; then
   (<>*f).x = I.(f.x) by FUNCT_1:13;
   hence A2: (<>*f).x = <* f.x *> by PDIFF_1:1;
   x in dom <>*f by A1,Th3; then
   (<>*f)/.x = (<>*f).x by PARTFUN1:def 6;
   hence (<>*f)/.x = <* f/.x *> by A1,A2,PARTFUN1:def 6;
end;
