reserve n,m,k for Nat;
reserve r,r1 for Real;
reserve f,seq,seq1 for Real_Sequence;
reserve x,y for set;
reserve e1,e2 for ExtReal;
reserve Nseq for increasing sequence of NAT;

:::theorem
:::  incl NAT is increasing natural-valued by Lm10;

registration
  cluster -> natural-valued for FinSequence of NAT;
  coherence;
end;

begin :: moved from GOBOARD1, 2010.03.01, A.T.

reserve v for FinSequence of REAL,
  r,s for Real,
