reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;

theorem Th45:
  (<*p1*>^f)/^1 = f
proof
A1: (<*p1*>^f)/.1 = p1 by FINSEQ_5:15;
  1 in Seg 1;
  then
A2: 1 in dom<*p1*> by FINSEQ_1:38;
  dom<*p1*> c= dom(<*p1*>^f) by FINSEQ_1:26;
  then <*(<*p1*>^f)/.(0+1)*>^((<*p1*>^f)/^1) = (<*p1*>^f)/^0 by A2,FINSEQ_5:31
    .= <*p1*>^f;
  hence thesis by A1,FINSEQ_1:33;
end;
