reserve a,b,c for set;

theorem :: FINSEQ_6:50
  for D being non empty set,f being FinSequence of D st f=<*a,b*> holds
  f/^1=<*b*>
proof
  let D be non empty set,f be FinSequence of D;
A1: f is Function of (dom f),D by FINSEQ_2:26;
  assume
A2: f = <*a,b*>;
  then
A3: 1 in dom f & 2 in dom f by CALCUL_1:14;
  f.1=a & f.2=b by A2;
  then reconsider a2=a, b2=b as Element of D by A3,A1,FUNCT_2:5;
  f/^1 = <*a2,b2*>/^1 by A2
    .= <*b2*> by FINSEQ_6:46;
  hence thesis;
end;
