theorem Th20:
  not a on A & not b on B & not a on C & not b on C & not A,B,C
  are_concurrent & A,C,Q are_concurrent & not b on Q & A<>Q & a<>b & a on O & b
on O implies ex q st q on O & not q on A & not q on Q & IncProj(C,b,B)*IncProj(
  A,a,C) = IncProj(Q,b,B)*IncProj(A,q,Q)
proof
  assume
A1: ( not a on A)& not b on B & ( not a on C)& not b on C & ( not A,B,C
are_concurrent)& A,C,Q are_concurrent & ( not b on Q)& A<>Q & a<>b & a on O & b
  on O;
  then not B,C,O are_concurrent implies thesis by Lm1;
  hence thesis by A1,Lm2;
end;
