
theorem Lm1:
  for A be non empty closed_interval Subset of REAL
  holds the carrier of ClstoCmp(A) = A
proof
  let A be non empty closed_interval Subset of REAL;
  consider a,b be Real such that
A1: a <= b & [.a,b.] = A
    & ClstoCmp(A) = Closed-Interval-TSpace(a,b) by Def7ClstoCmp;
  thus the carrier of ClstoCmp(A) = A by A1,TOPMETR:10;
end;
