
theorem Th3:
for I be Interval, x be Real st x in I & x <> inf I & x <> sup I holds
 x in ].inf I,sup I.[
proof
    let I be Interval, x be Real;
    assume that
A1:  x in I and
A2:  x <> inf I and
A3:  x <> sup I;
    inf I <= x <= sup I by A1,XXREAL_2:61,62; then
    inf I < x < sup I by A2,A3,XXREAL_0:1;
    hence x in ].inf I,sup I.[ by XXREAL_1:4;
end;
