
theorem Th27:
  for X being non empty finite set for S1, S2 being Signature of X
for A1 being Circuit of X,S1 for A2 being Circuit of X,S2 holds A1 tolerates A2
proof
  let X be non empty finite set;
  let S1,S2 be Signature of X;
  let A1 be Circuit of X,S1;
  let A2 be Circuit of X,S2;
  thus S1 tolerates S2 by CIRCCOMB:47;
  the Sorts of A2 is constant & the_value_of the Sorts of A2 = X by Def10;
  then
A1: the Sorts of A2 = (dom the Sorts of A2)-->X by FUNCOP_1:80;
  the Sorts of A1 is constant & the_value_of the Sorts of A1 = X by Def10;
  then the Sorts of A1 = (dom the Sorts of A1)-->X by FUNCOP_1:80;
  hence the Sorts of A1 tolerates the Sorts of A2 by A1,FUNCOP_1:87;
  thus thesis by CIRCCOMB:48;
end;
