reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

theorem
  0c*R = i|->0c
proof
A1: rng R c= COMPLEX;
A2: R is i-element FinSequence of COMPLEX by FINSEQ_1:102;
  thus 0c*R = multcomplex[;](0c,(id COMPLEX)*R) by FUNCOP_1:34
    .= multcomplex[;](0c,R) by A1,RELAT_1:53
    .= i|->0c by A2,BINOP_2:1,FINSEQOP:76,SEQ_4:51,54;
end;
