This answer takes everything in the question at face value.
The actions of the authors will not be looked upon favorably by the journal or the StackExchange network.
You would be able to prove that the ideas have been taken from your post. Besides your email/other correspondence with the authors (hopefully this is recorded), similarities between content, terminology, symbols etc. should be adequate to build your case. Once this is done, the authors run afoul of journal requirements (not to plagiarise) and the StackExchange policy of sharing attribution to any content taken from here (more on this ahead).
As such, the journal should take some action, either requiring that your work be cited or that the paper itself be retracted. Whether or not they do this depends on many factors, such as the journal policy, the editor's conscientiousness, the strength of your argument and so on. The authors should, in my opinion, face some censure (at the least) for indulging in malpractice.
However, my primary concern is something else that you stated :
as I planned to include them in my second book
You should know that anything posted on the SE sites is automatically shared under a cc-by-sa license. This means that anyone is free to share (copy, redistribute) and adapt (remix, transform, build upon - even commercially) content from here, provided that the post-creator is attributed (by author name and by mentioning that the content was posted to SE). Details about attribution here and cc-by-sa here.
In your context, this means that your proofs could legally be used by anyone, so long as they mention that you posted it to SE at a certain link. They are free even to put this in their book and sell that book commercially. By 'remix', I suppose they could simply change some terminology, and then claim that they have 'built upon' your work, perfectly legally.
So while your indignation at being cheated out of credit is justified, your proofs posted online may not be quite as secure as you imagine. We all have different stands on how freely work should be shared, so this may be quite alright with you. To me, it would be a bit naive to share something under a cc-by-sa license when I intend to ultimately put that in a textbook.
However, @BryanKrause has pointed out that this may not be quite as naive as I thought. You, as the creator, are allowed to relicense SE content (when you put it in a textbook, for example). What you have already put out (on SE) can always be used by others under the original cc-by-sa license though. More details on this here.