theorem ThSTC0S7: :: WALLACE1:27

for x1, x2, x3, x4, x5, x6, x7 being set holds
( [<*x1,x2*>,xor2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*x1,x2*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*x2,x3*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*x3,x1*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*x5,x6*>,xor2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*x5,x6*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*x6,x7*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*x7,x5*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & GFA0AdderOutput (x1,x2,x3) in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & GFA0CarryOutput (x1,x2,x3) in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & GFA0AdderOutput (x5,x6,x7) in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & GFA0CarryOutput (x5,x6,x7) in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,xor2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*(GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7))*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*(GFA0AdderOutput (x5,x6,x7)),x4*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*x4,(GFA0AdderOutput (x1,x2,x3))*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & GFA0AdderOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4) in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4) in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*(GFA0CarryOutput (x1,x2,x3)),(GFA0CarryOutput (x5,x6,x7))*>,xor2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & GFA0AdderOutput ((GFA0CarryOutput (x1,x2,x3)),(GFA0CarryOutput (x5,x6,x7)),(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))) in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*(GFA0CarryOutput (x1,x2,x3)),(GFA0CarryOutput (x5,x6,x7))*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*(GFA0CarryOutput (x5,x6,x7)),(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & [<*(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4)),(GFA0CarryOutput (x1,x2,x3))*>,and2] in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) & GFA0CarryOutput ((GFA0CarryOutput (x1,x2,x3)),(GFA0CarryOutput (x5,x6,x7)),(GFA0CarryOutput ((GFA0AdderOutput (x1,x2,x3)),(GFA0AdderOutput (x5,x6,x7)),x4))) in InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) )