theorem ThSTC0S1a: :: WALLACE1:21

for x1, x2, x3, x4, x5, x6, x7 being set holds InnerVertices (STC0Str (x1,x2,x3,x4,x5,x6,x7)) = ((InnerVertices (STC0IStr (x1,x2,x3,x4,x5,x6,x7))) \/ {[<*(STC0ICarryOutputC1 (x1,x2,x3,x4,x5,x6,x7)),(STC0ICarryOutputC2 (x1,x2,x3,x4,x5,x6,x7))*>,xor2],(GFA0AdderOutput ((STC0ICarryOutputC1 (x1,x2,x3,x4,x5,x6,x7)),(STC0ICarryOutputC2 (x1,x2,x3,x4,x5,x6,x7)),(STC0ICarryOutputC3 (x1,x2,x3,x4,x5,x6,x7))))}) \/ {[<*(STC0ICarryOutputC1 (x1,x2,x3,x4,x5,x6,x7)),(STC0ICarryOutputC2 (x1,x2,x3,x4,x5,x6,x7))*>,and2],[<*(STC0ICarryOutputC2 (x1,x2,x3,x4,x5,x6,x7)),(STC0ICarryOutputC3 (x1,x2,x3,x4,x5,x6,x7))*>,and2],[<*(STC0ICarryOutputC3 (x1,x2,x3,x4,x5,x6,x7)),(STC0ICarryOutputC1 (x1,x2,x3,x4,x5,x6,x7))*>,and2],(GFA0CarryOutput ((STC0ICarryOutputC1 (x1,x2,x3,x4,x5,x6,x7)),(STC0ICarryOutputC2 (x1,x2,x3,x4,x5,x6,x7)),(STC0ICarryOutputC3 (x1,x2,x3,x4,x5,x6,x7))))}