let x1, x2, x3, x5, x6, x7 be non pair set ; :: thesis: ( x1 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x2 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x3 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x5 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x6 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x7 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) )
set S = STC0IIStr (x1,x2,x3,x5,x6,x7);
InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) = {x1,x2,x3,x5,x6,x7} by ThSTC0IIS4;
hence ( x1 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x2 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x3 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x5 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x6 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) & x7 in InputVertices (STC0IIStr (x1,x2,x3,x5,x6,x7)) ) by ENUMSET1:def 4; :: thesis: verum