let x, y, z be set ; :: thesis: InnerVertices (BitGFA2Str (x,y,z)) = (({[<*x,y*>,xor2c]} \/ {(GFA2AdderOutput (x,y,z))}) \/ {[<*x,y*>,and2a],[<*y,z*>,and2c],[<*z,x*>,nor2]}) \/ {(GFA2CarryOutput (x,y,z))}
set f1 = and2a ;
set f2 = and2c ;
set f3 = nor2 ;
set f0 = xor2c ;
set xyf0 = [<*x,y*>,xor2c];
set xyf1 = [<*x,y*>,and2a];
set yzf2 = [<*y,z*>,and2c];
set zxf3 = [<*z,x*>,nor2];
set S = BitGFA2Str (x,y,z);
set S1 = GFA2AdderStr (x,y,z);
set S2 = GFA2CarryStr (x,y,z);
set A1 = GFA2AdderOutput (x,y,z);
set A2 = GFA2CarryOutput (x,y,z);
thus InnerVertices (BitGFA2Str (x,y,z)) = (InnerVertices (GFA2AdderStr (x,y,z))) \/ (InnerVertices (GFA2CarryStr (x,y,z))) by FACIRC_1:27
.= ({[<*x,y*>,xor2c]} \/ {(GFA2AdderOutput (x,y,z))}) \/ (InnerVertices (GFA2CarryStr (x,y,z))) by Th87
.= ({[<*x,y*>,xor2c]} \/ {(GFA2AdderOutput (x,y,z))}) \/ ({[<*x,y*>,and2a],[<*y,z*>,and2c],[<*z,x*>,nor2]} \/ {(GFA2CarryOutput (x,y,z))}) by Th74
.= (({[<*x,y*>,xor2c]} \/ {(GFA2AdderOutput (x,y,z))}) \/ {[<*x,y*>,and2a],[<*y,z*>,and2c],[<*z,x*>,nor2]}) \/ {(GFA2CarryOutput (x,y,z))} by XBOOLE_1:4 ; :: thesis: verum