reserve x,y,c for set;

theorem Th7:
  [<*x,y*>,and2a] in InnerVertices BorrowStr(x,y,c) & [<*y,c*>,and2
  ] in InnerVertices BorrowStr(x,y,c) & [<*x,c*>,and2a] in InnerVertices
  BorrowStr(x,y,c)
proof
  [<*x,y*>,and2a] in InnerVertices 1GateCircStr(<*x,y*>,and2a) by FACIRC_1:47;
  then [<*x,y*>,and2a] in InnerVertices (1GateCircStr(<*x,y*>,and2a)+*
  1GateCircStr(<*y,c*>,and2)) by FACIRC_1:21;
  then
A1: [<*x,y*>,and2a] in InnerVertices BorrowIStr(x,y,c) by FACIRC_1:21;
  [<*y,c*>,and2 ] in InnerVertices 1GateCircStr(<*y,c*>,and2 ) by FACIRC_1:47;
  then [<*y,c*>,and2 ] in InnerVertices (1GateCircStr(<*x,y*>,and2a)+*
  1GateCircStr(<*y,c*>,and2)) by FACIRC_1:21;
  then
A2: [<*y,c*>,and2 ] in InnerVertices BorrowIStr(x,y,c) by FACIRC_1:21;
  [<*x,c*>,and2a] in InnerVertices 1GateCircStr(<*x,c*>,and2a) by FACIRC_1:47;
  then [<*x,c*>,and2a] in InnerVertices BorrowIStr(x,y,c) by FACIRC_1:21;
  hence thesis by A1,A2,FACIRC_1:21;
end;
