Re: [mizar] Union of two subgroups

[Victor Makarov <viktmak@gmail.com>]

Thanks, I'll check them out. 

On Tue, Nov 17, 2020 at 7:51 AM Adam Naumowicz <adamn@math.uwb.edu.pl> wrote:

Dear Victor,

On Mon, 16 Nov 2020, Victor Makarov wrote:

> Dear All:
>
> I cannot find in MML a theorem that the union of two subgroups is  a
> subgroup iff  one of the subgroups is a subset of the other subgroup.
>
> The same question about the product of two subgroups H and K:
>
> H*K is a subgroup iff H*K = K*H.

This may not be exactly what you want, but have you checked these
theorems:

theorem :: GROUP_4:50
   H1 "\/" H2 = gr(H1 * H2);

theorem :: GROUP_4:51
   H1 * H2 = H2 * H1 implies the carrier of H1 "\/" H2 = H1 * H2;

?

Best regards,

Adam Naumowicz

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