reserve a,b,c,d,m,x,n,j,k,l for Nat,
  t,u,v,z for Integer,
  f,F for FinSequence of NAT;
reserve p,q,r,s for real number;
reserve a,b,c,d,m,x,n,k,l for Nat,
  t,z for Integer,
  f,F,G for FinSequence of REAL;
reserve q,r,s for real number;
reserve D for set;

theorem Th7:
  n in dom f & 1 <= m & m <= n implies f.m = (f|n).m
  proof
    assume
    A1: n in dom f & 1 <= m & m <= n; then
    m in Seg n;
    hence thesis by A1, RFINSEQ:6;
  end;
