let x, y, z be set ; :: thesis: ( [<*x,y*>,nor2] in InnerVertices (GFA3CarryStr (x,y,z)) & [<*y,z*>,nor2] in InnerVertices (GFA3CarryStr (x,y,z)) & [<*z,x*>,nor2] in InnerVertices (GFA3CarryStr (x,y,z)) & GFA3CarryOutput (x,y,z) in InnerVertices (GFA3CarryStr (x,y,z)) )
set f1 = nor2 ;
set f2 = nor2 ;
set f3 = nor2 ;
set xy = [<*x,y*>,nor2];
set yz = [<*y,z*>,nor2];
set zx = [<*z,x*>,nor2];
InnerVertices (GFA3CarryStr (x,y,z)) = {[<*x,y*>,nor2],[<*y,z*>,nor2],[<*z,x*>,nor2]} \/ {(GFA3CarryOutput (x,y,z))} by Th106
.= {[<*x,y*>,nor2],[<*y,z*>,nor2],[<*z,x*>,nor2],(GFA3CarryOutput (x,y,z))} by ENUMSET1:6 ;
hence ( [<*x,y*>,nor2] in InnerVertices (GFA3CarryStr (x,y,z)) & [<*y,z*>,nor2] in InnerVertices (GFA3CarryStr (x,y,z)) & [<*z,x*>,nor2] in InnerVertices (GFA3CarryStr (x,y,z)) & GFA3CarryOutput (x,y,z) in InnerVertices (GFA3CarryStr (x,y,z)) ) by ENUMSET1:def 2; :: thesis: verum