set f1 = and2c ;
set f2 = and2a ;
set f3 = and2 ;
let x, y, z be set ; :: thesis: ( x <> [<*y,z*>,and2a ] & y <> [<*z,x*>,and2 ] & z <> [<*x,y*>,and2c ] implies ( x in InputVertices (GFA1CarryStr x,y,z) & y in InputVertices (GFA1CarryStr x,y,z) & z in InputVertices (GFA1CarryStr x,y,z) ) )
assume A1: ( x <> [<*y,z*>,and2a ] & y <> [<*z,x*>,and2 ] & z <> [<*x,y*>,and2c ] ) ; :: thesis: ( x in InputVertices (GFA1CarryStr x,y,z) & y in InputVertices (GFA1CarryStr x,y,z) & z in InputVertices (GFA1CarryStr x,y,z) )
InputVertices (GFA1CarryStr x,y,z) = {x,y,z} by A1, Th53;
hence ( x in InputVertices (GFA1CarryStr x,y,z) & y in InputVertices (GFA1CarryStr x,y,z) & z in InputVertices (GFA1CarryStr x,y,z) ) by ENUMSET1:def 1; :: thesis: verum