reserve

  k,n,m,i,j for Element of NAT,
  K for Field;
reserve L for non empty addLoopStr;
reserve G for non empty multLoopStr;

theorem Th24:
  for i, n being Nat st 1<=i & i<=n holds (Base_FinSeq(K,n,i)).i= 1.K
proof
  let i, n be Nat;
  assume
A1: 1<=i & i<=n;
A2: len (n |-> (0.K))=n by CARD_1:def 7;
  len (Replace((n |-> (0.K)),i,1.K)) = len (n |-> 0.K) by FINSEQ_7:5
    .= n by CARD_1:def 7;
  hence (Base_FinSeq(K,n,i)).i = (Replace((n |-> (0.K)),i,1.K))/.i by A1,
FINSEQ_4:15
    .= 1.K by A1,A2,FINSEQ_7:8;
end;
