
theorem Th12:
  for x,y,c being set holds InnerVertices BorrowIStr(x,y,c) =
  {[<*x,y*>,and2a], [<*y,c*>,and2], [<*x,c*>,and2a]}
proof
  let x,y,c be set;
A1: 1GateCircStr(<*x,y*>,and2a) +* 1GateCircStr(<*y,c*>,and2) tolerates
  1GateCircStr(<*x,c*>,and2a) by CIRCCOMB:47;
A2: 1GateCircStr(<*x,y*>,and2a) tolerates 1GateCircStr(<*y,c*>,and2)
  by CIRCCOMB:47;
  InnerVertices BorrowIStr(x,y,c) =
  InnerVertices(1GateCircStr(<*x,y*>,and2a) +* 1GateCircStr(<*y,c*>,and2)) \/
  InnerVertices(1GateCircStr(<*x,c*>,and2a)) by A1,CIRCCOMB:11
    .= InnerVertices(1GateCircStr(<*x,y*>,and2a)) \/
  InnerVertices(1GateCircStr(<*y,c*>,and2)) \/
  InnerVertices(1GateCircStr(<*x,c*>,and2a)) by A2,CIRCCOMB:11
    .= {[<*x,y*>,and2a]} \/ InnerVertices(1GateCircStr(<*y,c*>,and2)) \/
  InnerVertices(1GateCircStr(<*x,c*>,and2a)) by CIRCCOMB:42
    .= {[<*x,y*>,and2a]} \/ {[<*y,c*>,and2]} \/
  InnerVertices(1GateCircStr(<*x,c*>,and2a)) by CIRCCOMB:42
    .= {[<*x,y*>,and2a]} \/ {[<*y,c*>,and2]} \/ {[<*x,c*>,and2a]}
  by CIRCCOMB:42
    .= {[<*x,y*>,and2a],[<*y,c*>,and2]} \/ {[<*x,c*>,and2a]}
  by ENUMSET1:1
    .= {[<*x,y*>,and2a],[<*y,c*>,and2],[<*x,c*>,and2a]}
  by ENUMSET1:3;
  hence thesis;
end;
