theorem
  <* a,b,c *> |^ d = <* a |^ d,b |^ d,c |^ d *>
proof
  thus <* a,b,c *> |^ d = (<* a *> ^ <* b,c *>) |^ d by FINSEQ_1:43
    .= (<* a *> |^ d) ^ (<* b,c *> |^ d) by Th9
    .= <* a *> |^ d ^ <* b |^ d,c |^ d *> by Th12
    .= <* a |^ d *> ^ <* b |^ d,c |^ d *> by Th11
    .= <* a |^ d,b |^ d,c |^ d *> by FINSEQ_1:43;
end;
