reserve x,y,z,c for object,
  f for Function of 2-tuples_on BOOLEAN, BOOLEAN;
reserve s for State of 2GatesCircuit(x,y,c,f);

theorem Th74:
  for x,y,c being non pair object holds x in InputVertices
MajorityStr(x,y,c) & y in InputVertices MajorityStr(x,y,c) & c in InputVertices
  MajorityStr(x,y,c)
proof
  let x,y,c be non pair object;
  assume
A1: not thesis;
A2: c in the carrier of MajorityStr(x,y,c) by Th72;
A3: InnerVertices MajorityStr(x,y,c) is Relation by Th67;
  x in the carrier of MajorityStr(x,y,c) & y in the carrier of MajorityStr
  (x,y,c) by Th72;
  then
  x in InnerVertices MajorityStr(x,y,c) or y in InnerVertices MajorityStr(
  x,y,c) or c in InnerVertices MajorityStr(x,y,c) by A2,A1,XBOOLE_0:def 5;
  then
  (ex a,b being object st x = [a,b]) or
(ex a,b being object st y = [a,b]) or ex
  a,b being object st c = [a,b] by A3,RELAT_1:def 1;
  hence contradiction;
end;
