reserve n,n1,m,m1,k for Nat;
reserve x,X,X1 for set;
reserve g,g1,g2,t,x0,x1,x2 for Complex;
reserve s1,s2,q1,seq,seq1,seq2,seq3 for Complex_Sequence;
reserve Y for Subset of COMPLEX;
reserve f,f1,f2,h,h1,h2 for PartFunc of COMPLEX,COMPLEX;
reserve p,r,s for Real;
reserve Ns,Nseq for increasing sequence of NAT;

theorem Th26:
  seq is constant implies seq is convergent
proof
  assume seq is constant;
  then consider t being Element of COMPLEX such that
A1: for n being Nat holds seq.n=t by VALUED_0:def 18;
  take g=t;
  let p such that
A2: 0<p;
  take n=0;
  let m such that
  n<=m;
  |.(seq.m)-g.|=|.t-g.| by A1
    .=0 by COMPLEX1:44;
  hence |.(seq.m)-g.|<p by A2;
end;
