reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve L,M for Element of NAT;
reserve f for Function of A,B;
reserve f for Function;
reserve x1,x2,x3,x4,x5 for object;
reserve p for FinSequence;
reserve ND for non empty set;
reserve y1,y2,y3,y4,y5 for Element of ND;

theorem
  for D being non empty set, p,q being FinSequence of D, i being Element
  of NAT st p c= q & 1 <= i & i <= len p holds q.i = p.i
proof
  let D be non empty set, p,q be FinSequence of D, i be Element of NAT;
  assume p c= q;
  then
A1: ex p9 being FinSequence of D st p ^ p9 = q by Th80;
  assume 1 <= i & i <= len p;
  hence thesis by A1,FINSEQ_1:64;
end;
