reserve r for Real;
reserve a, b for Real;
reserve T for non empty TopSpace;
reserve A for non empty SubSpace of T;
reserve P,Q for Subset of T,
  p for Point of T;
reserve M for non empty MetrSpace,
  p for Point of M;
reserve A for non empty SubSpace of M;

theorem Th10:
  a <= b implies the carrier of Closed-Interval-MSpace(a,b) = [. a ,b .]
proof
  assume
A1: a <= b;
  then reconsider P = [. a,b .] as non empty Subset of RealSpace by XXREAL_1:1;
  thus the carrier of Closed-Interval-MSpace(a,b) = the carrier of RealSpace |
  P by A1,Def3
    .= [. a,b .] by Def2;
end;
