let x, y, z be set ; ( [<*x,y*>,xor2c] in InnerVertices (GFA2AdderStr (x,y,z)) & GFA2AdderOutput (x,y,z) in InnerVertices (GFA2AdderStr (x,y,z)) )
set S1 = GFA1AdderStr (x,y,z);
GFA2AdderStr (x,y,z) = GFA1AdderStr (x,y,z)
;
hence
( [<*x,y*>,xor2c] in InnerVertices (GFA2AdderStr (x,y,z)) & GFA2AdderOutput (x,y,z) in InnerVertices (GFA2AdderStr (x,y,z)) )
by Th57; verum