theorem Th36:
  l in Seg n & len pK = n & len qK = n implies Det(RLine(A,l,pK+qK
  )) = Det(RLine(A,l,pK)) + Det(RLine(A,l,qK))
proof
  assume that
A1: l in Seg n and
A2: len pK=n and
A3: len qK=n;
  pK is Element of (len pK)-tuples_on the carrier of K by FINSEQ_2:92;
  then
A4: 1_K*pK=pK by FVSUM_1:57;
  qK is Element of (len pK)-tuples_on the carrier of K by A2,A3,FINSEQ_2:92;
  then 1_K*qK=qK by FVSUM_1:57;
  hence Det(RLine(A,l,pK+qK))=1_K*Det(RLine(A,l,pK))+1_K*Det(RLine(A,l,qK)) by
A1,A2,A3,A4,Th33
    .= Det(RLine(A,l,pK))+1_K*Det(RLine(A,l,qK))
    .= Det(RLine(A,l,pK))+Det(RLine(A,l,qK));
end;
