theorem Th12:
  <* a,b *> |^ c = <* a |^ c,b |^ c *>
proof
  thus <* a,b *> |^ c = (<* a *> ^ <* b *>) |^ c by FINSEQ_1:def 9
    .= (<* a *> |^ c) ^ (<* b *> |^ c) by Th9
    .= <* a |^ c *> ^ (<* b *> |^ c) by Th11
    .= <* a |^ c *> ^ <* b |^ c *> by Th11
    .= <* a |^ c, b |^ c *> by FINSEQ_1:def 9;
end;
