reserve a, b, r, s for Real;
reserve n, m for Nat,
  F for Subset-Family of Closed-Interval-TSpace (r,s);
reserve C for IntervalCover of F;
reserve G for IntervalCoverPts of C;

theorem Th61:
  F is Cover of Closed-Interval-TSpace(r,s) & F is open connected
  & r <= s & len C = 1 implies G = <*r,s*>
proof
  assume that
A1: F is Cover of Closed-Interval-TSpace(r,s) & F is open & F is
  connected & r <= s and
A2: len C = 1;
A3: G.1 = r by A1,Def3;
A4: len G = len C + 1 by A1,Def3;
  then G.2 = s by A1,A2,Def3;
  hence thesis by A2,A4,A3,FINSEQ_1:44;
end;
