let f be set ; for x, y being non pair set holds not InputVertices (1GateCircStr <*x,y*>,f) is with_pair
let x, y be non pair set ; not InputVertices (1GateCircStr <*x,y*>,f) is with_pair
set p = <*x,y*>;
let z be pair set ; FACIRC_1:def 2 not z in InputVertices (1GateCircStr <*x,y*>,f)
assume A1:
z in InputVertices (1GateCircStr <*x,y*>,f)
; contradiction
InputVertices (1GateCircStr <*x,y*>,f) = {x,y}
by Th40;
hence
contradiction
by A1, TARSKI:def 2; verum