set f1 = and2a ;
set f2 = and2c ;
set f3 = nor2 ;
let x, y, z be set ; ( x <> [<*y,z*>,and2c] & y <> [<*z,x*>,nor2] & z <> [<*x,y*>,and2a] implies ( x in InputVertices (GFA2CarryStr (x,y,z)) & y in InputVertices (GFA2CarryStr (x,y,z)) & z in InputVertices (GFA2CarryStr (x,y,z)) ) )
assume
( x <> [<*y,z*>,and2c] & y <> [<*z,x*>,nor2] & z <> [<*x,y*>,and2a] )
; ( x in InputVertices (GFA2CarryStr (x,y,z)) & y in InputVertices (GFA2CarryStr (x,y,z)) & z in InputVertices (GFA2CarryStr (x,y,z)) )
then
InputVertices (GFA2CarryStr (x,y,z)) = {x,y,z}
by Th77;
hence
( x in InputVertices (GFA2CarryStr (x,y,z)) & y in InputVertices (GFA2CarryStr (x,y,z)) & z in InputVertices (GFA2CarryStr (x,y,z)) )
by ENUMSET1:def 1; verum