theorem :: BORSUK_5:67

for A being Subset of R^1
for a, b, c, d being Real st a < b & b < c & A = (((].-infty,a.[ \/ ].a,b.]) \/ (IRRAT (b,c))) \/ {c}) \/ {d} holds
Cl A = ].-infty,c.] \/ {d}