
theorem Th13:
  for S1,S2 being non empty ManySortedSign st S1 tolerates S2 for
v1 being Vertex of S1 st v1 in InputVertices (S1+*S2) holds v1 in InputVertices
  S1
proof
  let S1,S2 be non empty ManySortedSign such that
  the Arity of S1 tolerates the Arity of S2 and
A1: the ResultSort of S1 tolerates the ResultSort of S2;
  set S = S1+*S2, R = the ResultSort of S;
  set R1 = the ResultSort of S1, R2 = the ResultSort of S2;
  R = R1+*R2 by Def2;
  then R1 c= R by A1,FUNCT_4:28;
  then
A2: rng R1 c= rng R by RELAT_1:11;
  let v1 be Vertex of S1;
  assume v1 in InputVertices S;
  then not v1 in rng R1 by A2,XBOOLE_0:def 5;
  hence thesis by XBOOLE_0:def 5;
end;
