
theorem Th21:
  for S1,S2 being non empty ManySortedSign
  st S1 tolerates S2 & InputVertices S1 = InputVertices S2
  holds InputVertices (S1+*S2) = InputVertices S1
proof
  let S1,S2 be non empty ManySortedSign such that
A1: S1 tolerates S2 and
A2: InputVertices S1 = InputVertices S2;
A3: InnerVertices S1 misses InputVertices S1 by XBOOLE_1:79;
A4: InnerVertices S2 misses InputVertices S2 by XBOOLE_1:79;
  thus
  InputVertices (S1+*S2) = ((InputVertices S1)\(InnerVertices S2)) \/
  ((InputVertices S2)\(InnerVertices S1)) by A1,CIRCCMB2:5
    .= (InputVertices S1) \/
  ((InputVertices S2)\(InnerVertices S1)) by A2,A4,XBOOLE_1:83
    .= InputVertices S1 \/ InputVertices S2 by A2,A3,XBOOLE_1:83
    .= InputVertices S1 by A2;
end;
