set f1 = and2 ;
set f2 = and2 ;
set f3 = and2 ;
let x, y, z be set ; :: thesis: ( [<*x,y*>,and2 ] in InnerVertices (GFA0CarryStr x,y,z) & [<*y,z*>,and2 ] in InnerVertices (GFA0CarryStr x,y,z) & [<*z,x*>,and2 ] in InnerVertices (GFA0CarryStr x,y,z) & GFA0CarryOutput x,y,z in InnerVertices (GFA0CarryStr x,y,z) )
set xy = [<*x,y*>,and2 ];
set yz = [<*y,z*>,and2 ];
set zx = [<*z,x*>,and2 ];
InnerVertices (GFA0CarryStr x,y,z) = {[<*x,y*>,and2 ],[<*y,z*>,and2 ],[<*z,x*>,and2 ]} \/ {(GFA0CarryOutput x,y,z)} by Th14
.= {[<*x,y*>,and2 ],[<*y,z*>,and2 ],[<*z,x*>,and2 ],(GFA0CarryOutput x,y,z)} by ENUMSET1:46 ;
hence ( [<*x,y*>,and2 ] in InnerVertices (GFA0CarryStr x,y,z) & [<*y,z*>,and2 ] in InnerVertices (GFA0CarryStr x,y,z) & [<*z,x*>,and2 ] in InnerVertices (GFA0CarryStr x,y,z) & GFA0CarryOutput x,y,z in InnerVertices (GFA0CarryStr x,y,z) ) by ENUMSET1:def 2; :: thesis: verum