{"action":"closed","number":494,"pull_request":{"url":"https://api.github.com/repos/metamath/set.mm/pulls/494","id":211528786,"node_id":"MDExOlB1bGxSZXF1ZXN0MjExNTI4Nzg2","html_url":"https://github.com/metamath/set.mm/pull/494","diff_url":"https://github.com/metamath/set.mm/pull/494.diff","patch_url":"https://github.com/metamath/set.mm/pull/494.patch","issue_url":"https://api.github.com/repos/metamath/set.mm/issues/494","number":494,"state":"closed","locked":false,"title":"Add \"Theorems requiring subset and intersection existence\" section to iset.mm","user":{"login":"jkingdon","id":16878,"node_id":"MDQ6VXNlcjE2ODc4","avatar_url":"https://avatars0.githubusercontent.com/u/16878?v=4","gravatar_id":"","url":"https://api.github.com/users/jkingdon","html_url":"https://github.com/jkingdon","followers_url":"https://api.github.com/users/jkingdon/followers","following_url":"https://api.github.com/users/jkingdon/following{/other_user}","gists_url":"https://api.github.com/users/jkingdon/gists{/gist_id}","starred_url":"https://api.github.com/users/jkingdon/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/jkingdon/subscriptions","organizations_url":"https://api.github.com/users/jkingdon/orgs","repos_url":"https://api.github.com/users/jkingdon/repos","events_url":"https://api.github.com/users/jkingdon/events{/privacy}","received_events_url":"https://api.github.com/users/jkingdon/received_events","type":"User","site_admin":false},"body":"Add  `alexnim` (one direction of `alexn` from set.mm).\r\n\r\nBreak `intex` into two theorems: `inteximm` is the forward direction (but for inhabited rather than non-empty classes) and `intexr` is the reverse direction.\r\n\r\nThe reverse direction of `intnex` is the one we already have a proof for. Although it is pretty much trivial, just include that one and name it `intnexr` .\r\n\r\nIntuitionize `intexab` and `intexrab` in iset.mm. In both cases, prove the forward direction and accordingly\r\nrename to `intexabim` and `intexrabim` respectively.\r\n\r\nRename `iinexg` to `iinexgm` and change non-empty to inhabited. Also, the proof, although basically the same in structure, needs changes throughout for intuitionistic logic. Specifically, `r19.35-1` in place of `r19.35` , `r19.2m` in place of `r19.2z` , `abid` in place of `abn0` , and `inteximm` in place of `intex` (which also means we need a variable change).\r\n\r\nRemove `intabs` from iset.mm. The proof is not easily intuitionized and it is only used once\r\nin set.mm (some distance in the 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