let x1, x2, x3, x4, x5, x6, x7 be set ; :: thesis: InnerVertices (STC0IStr (x1,x2,x3,x4,x5,x6,x7)) = (((({[<*x1,x2*>,xor2],(GFA0AdderOutput (x1,x2,x3))} \/ {[<*x1,x2*>,and2],[<*x2,x3*>,and2],[<*x3,x1*>,and2],(GFA0CarryOutput (x1,x2,x3))}) \/ {[<*x5,x6*>,xor2],(GFA0AdderOutput (x5,x6,x7))}) \/ {[<*x5,x6*>,and2],[<*x6,x7*>,and2],[<*x7,x5*>,and2],(GFA0CarryOutput (x5,x6,x7))}) \/ {[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,xor2],(GFA0AdderOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))}) \/ {[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,and2],[<*(GFA0AdderOutput (x5,x6,x7)),x4*>,and2],[<*x4,(GFA0AdderOutput (x1,x2,x3))*>,and2],(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))}
set S = STC0IStr (x1,x2,x3,x4,x5,x6,x7);
set S1 = STC0IIStr (x1,x2,x3,x5,x6,x7);
set A1 = GFA0AdderOutput (x1,x2,x3);
set C1 = GFA0CarryOutput (x1,x2,x3);
set A2 = GFA0AdderOutput (x5,x6,x7);
set C2 = GFA0CarryOutput (x5,x6,x7);
set x1x20 = [<*x1,x2*>,xor2];
set x1x2 = [<*x1,x2*>,and2];
set x2x3 = [<*x2,x3*>,and2];
set x3x1 = [<*x3,x1*>,and2];
set x5x60 = [<*x5,x6*>,xor2];
set x5x6 = [<*x5,x6*>,and2];
set x6x7 = [<*x6,x7*>,and2];
set x7x5 = [<*x7,x5*>,and2];
set S2 = BitGFA0Str ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4);
set A3 = GFA0AdderOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4);
set C3 = GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4);
set A1A20 = [<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,xor2];
set A1A2 = [<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,and2];
set A2x4 = [<*(GFA0AdderOutput (x5,x6,x7)),x4*>,and2];
set x4A1 = [<*x4,(GFA0AdderOutput (x1,x2,x3))*>,and2];
STC0IIStr (x1,x2,x3,x5,x6,x7) tolerates BitGFA0Str ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4) by CIRCCOMB:47;
hence InnerVertices (STC0IStr (x1,x2,x3,x4,x5,x6,x7)) = (InnerVertices (STC0IIStr (x1,x2,x3,x5,x6,x7))) \/ (InnerVertices (BitGFA0Str ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))) by CIRCCOMB:11
.= ((({[<*x1,x2*>,xor2],(GFA0AdderOutput (x1,x2,x3))} \/ {[<*x1,x2*>,and2],[<*x2,x3*>,and2],[<*x3,x1*>,and2],(GFA0CarryOutput (x1,x2,x3))}) \/ {[<*x5,x6*>,xor2],(GFA0AdderOutput (x5,x6,x7))}) \/ {[<*x5,x6*>,and2],[<*x6,x7*>,and2],[<*x7,x5*>,and2],(GFA0CarryOutput (x5,x6,x7))}) \/ (InnerVertices (BitGFA0Str ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))) by ThSTC0IIS1
.= ((({[<*x1,x2*>,xor2],(GFA0AdderOutput (x1,x2,x3))} \/ {[<*x1,x2*>,and2],[<*x2,x3*>,and2],[<*x3,x1*>,and2],(GFA0CarryOutput (x1,x2,x3))}) \/ {[<*x5,x6*>,xor2],(GFA0AdderOutput (x5,x6,x7))}) \/ {[<*x5,x6*>,and2],[<*x6,x7*>,and2],[<*x7,x5*>,and2],(GFA0CarryOutput (x5,x6,x7))}) \/ ((({[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,xor2]} \/ {(GFA0AdderOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))}) \/ {[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,and2],[<*(GFA0AdderOutput (x5,x6,x7)),x4*>,and2],[<*x4,(GFA0AdderOutput (x1,x2,x3))*>,and2]}) \/ {(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))}) by GFACIRC1:31
.= ((({[<*x1,x2*>,xor2],(GFA0AdderOutput (x1,x2,x3))} \/ {[<*x1,x2*>,and2],[<*x2,x3*>,and2],[<*x3,x1*>,and2],(GFA0CarryOutput (x1,x2,x3))}) \/ {[<*x5,x6*>,xor2],(GFA0AdderOutput (x5,x6,x7))}) \/ {[<*x5,x6*>,and2],[<*x6,x7*>,and2],[<*x7,x5*>,and2],(GFA0CarryOutput (x5,x6,x7))}) \/ (({[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,xor2],(GFA0AdderOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))} \/ {[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,and2],[<*(GFA0AdderOutput (x5,x6,x7)),x4*>,and2],[<*x4,(GFA0AdderOutput (x1,x2,x3))*>,and2]}) \/ {(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))}) by ENUMSET1:1
.= ((({[<*x1,x2*>,xor2],(GFA0AdderOutput (x1,x2,x3))} \/ {[<*x1,x2*>,and2],[<*x2,x3*>,and2],[<*x3,x1*>,and2],(GFA0CarryOutput (x1,x2,x3))}) \/ {[<*x5,x6*>,xor2],(GFA0AdderOutput (x5,x6,x7))}) \/ {[<*x5,x6*>,and2],[<*x6,x7*>,and2],[<*x7,x5*>,and2],(GFA0CarryOutput (x5,x6,x7))}) \/ ({[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,xor2],(GFA0AdderOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))} \/ ({[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,and2],[<*(GFA0AdderOutput (x5,x6,x7)),x4*>,and2],[<*x4,(GFA0AdderOutput (x1,x2,x3))*>,and2]} \/ {(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))})) by XBOOLE_1:4
.= ((({[<*x1,x2*>,xor2],(GFA0AdderOutput (x1,x2,x3))} \/ {[<*x1,x2*>,and2],[<*x2,x3*>,and2],[<*x3,x1*>,and2],(GFA0CarryOutput (x1,x2,x3))}) \/ {[<*x5,x6*>,xor2],(GFA0AdderOutput (x5,x6,x7))}) \/ {[<*x5,x6*>,and2],[<*x6,x7*>,and2],[<*x7,x5*>,and2],(GFA0CarryOutput (x5,x6,x7))}) \/ ({[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,xor2],(GFA0AdderOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))} \/ {[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,and2],[<*(GFA0AdderOutput (x5,x6,x7)),x4*>,and2],[<*x4,(GFA0AdderOutput (x1,x2,x3))*>,and2],(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))}) by ENUMSET1:6
.= (((({[<*x1,x2*>,xor2],(GFA0AdderOutput (x1,x2,x3))} \/ {[<*x1,x2*>,and2],[<*x2,x3*>,and2],[<*x3,x1*>,and2],(GFA0CarryOutput (x1,x2,x3))}) \/ {[<*x5,x6*>,xor2],(GFA0AdderOutput (x5,x6,x7))}) \/ {[<*x5,x6*>,and2],[<*x6,x7*>,and2],[<*x7,x5*>,and2],(GFA0CarryOutput (x5,x6,x7))}) \/ {[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,xor2],(GFA0AdderOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))}) \/ {[<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,and2],[<*(GFA0AdderOutput (x5,x6,x7)),x4*>,and2],[<*x4,(GFA0AdderOutput (x1,x2,x3))*>,and2],(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))} by XBOOLE_1:4 ;
:: thesis: verum