set f0 = xor2c ;
set f1 = and2c ;
set f2 = and2a ;
set f3 = and2 ;
let x, y, z be set ; :: thesis: ( [<*x,y*>,xor2c ] in InnerVertices (BitGFA1Str x,y,z) & GFA1AdderOutput x,y,z in InnerVertices (BitGFA1Str x,y,z) & [<*x,y*>,and2c ] in InnerVertices (BitGFA1Str x,y,z) & [<*y,z*>,and2a ] in InnerVertices (BitGFA1Str x,y,z) & [<*z,x*>,and2 ] in InnerVertices (BitGFA1Str x,y,z) & GFA1CarryOutput x,y,z in InnerVertices (BitGFA1Str x,y,z) )
set xyf0 = [<*x,y*>,xor2c ];
set xyf1 = [<*x,y*>,and2c ];
set yzf2 = [<*y,z*>,and2a ];
set zxf3 = [<*z,x*>,and2 ];
set S = BitGFA1Str x,y,z;
set A1 = GFA1AdderOutput x,y,z;
set A2 = GFA1CarryOutput x,y,z;
InnerVertices (BitGFA1Str x,y,z) = (({[<*x,y*>,xor2c ]} \/ {(GFA1AdderOutput x,y,z)}) \/ {[<*x,y*>,and2c ],[<*y,z*>,and2a ],[<*z,x*>,and2 ]}) \/ {(GFA1CarryOutput x,y,z)} by Th76
.= ({[<*x,y*>,xor2c ],(GFA1AdderOutput x,y,z)} \/ {[<*x,y*>,and2c ],[<*y,z*>,and2a ],[<*z,x*>,and2 ]}) \/ {(GFA1CarryOutput x,y,z)} by ENUMSET1:41
.= {[<*x,y*>,xor2c ],(GFA1AdderOutput x,y,z),[<*x,y*>,and2c ],[<*y,z*>,and2a ],[<*z,x*>,and2 ]} \/ {(GFA1CarryOutput x,y,z)} by ENUMSET1:48
.= {[<*x,y*>,xor2c ],(GFA1AdderOutput x,y,z),[<*x,y*>,and2c ],[<*y,z*>,and2a ],[<*z,x*>,and2 ],(GFA1CarryOutput x,y,z)} by ENUMSET1:55 ;
hence ( [<*x,y*>,xor2c ] in InnerVertices (BitGFA1Str x,y,z) & GFA1AdderOutput x,y,z in InnerVertices (BitGFA1Str x,y,z) & [<*x,y*>,and2c ] in InnerVertices (BitGFA1Str x,y,z) & [<*y,z*>,and2a ] in InnerVertices (BitGFA1Str x,y,z) & [<*z,x*>,and2 ] in InnerVertices (BitGFA1Str x,y,z) & GFA1CarryOutput x,y,z in InnerVertices (BitGFA1Str x,y,z) ) by ENUMSET1:def 4; :: thesis: verum