let x, y, z be set ; ( [<*x,y*>,xor2] in InnerVertices (GFA0AdderStr (x,y,z)) & GFA0AdderOutput (x,y,z) in InnerVertices (GFA0AdderStr (x,y,z)) )
set f = xor2 ;
set S = GFA0AdderStr (x,y,z);
InnerVertices (GFA0AdderStr (x,y,z)) =
{[<*x,y*>,xor2]} \/ {(GFA0AdderOutput (x,y,z))}
by Th24
.=
{[<*x,y*>,xor2],(GFA0AdderOutput (x,y,z))}
by ENUMSET1:1
;
hence
( [<*x,y*>,xor2] in InnerVertices (GFA0AdderStr (x,y,z)) & GFA0AdderOutput (x,y,z) in InnerVertices (GFA0AdderStr (x,y,z)) )
by TARSKI:def 2; verum