set f = xor2c ;
let x, y, z be set ; ( z <> [<*x,y*>,xor2c] implies ( x in InputVertices (GFA1AdderStr (x,y,z)) & y in InputVertices (GFA1AdderStr (x,y,z)) & z in InputVertices (GFA1AdderStr (x,y,z)) ) )
assume A1:
z <> [<*x,y*>,xor2c]
; ( x in InputVertices (GFA1AdderStr (x,y,z)) & y in InputVertices (GFA1AdderStr (x,y,z)) & z in InputVertices (GFA1AdderStr (x,y,z)) )
set S = GFA1AdderStr (x,y,z);
InputVertices (GFA1AdderStr (x,y,z)) = {x,y,z}
by A1, FACIRC_1:57;
hence
( x in InputVertices (GFA1AdderStr (x,y,z)) & y in InputVertices (GFA1AdderStr (x,y,z)) & z in InputVertices (GFA1AdderStr (x,y,z)) )
by ENUMSET1:def 1; verum