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 ( 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)) )
then InputVertices (GFA1CarryStr (x,y,z)) = {x,y,z} by Th45;
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