{"action":"closed","issue":{"url":"https://api.github.com/repos/HoTT/HoTT/issues/671","labels_url":"https://api.github.com/repos/HoTT/HoTT/issues/671/labels{/name}","comments_url":"https://api.github.com/repos/HoTT/HoTT/issues/671/comments","events_url":"https://api.github.com/repos/HoTT/HoTT/issues/671/events","html_url":"https://github.com/HoTT/HoTT/issues/671","id":53492680,"number":671,"title":"Projecting truncatedness?","user":{"login":"JasonGross","id":396076,"avatar_url":"https://avatars.githubusercontent.com/u/396076?v=3","gravatar_id":"","url":"https://api.github.com/users/JasonGross","html_url":"https://github.com/JasonGross","followers_url":"https://api.github.com/users/JasonGross/followers","following_url":"https://api.github.com/users/JasonGross/following{/other_user}","gists_url":"https://api.github.com/users/JasonGross/gists{/gist_id}","starred_url":"https://api.github.com/users/JasonGross/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/JasonGross/subscriptions","organizations_url":"https://api.github.com/users/JasonGross/orgs","repos_url":"https://api.github.com/users/JasonGross/repos","events_url":"https://api.github.com/users/JasonGross/events{/privacy}","received_events_url":"https://api.github.com/users/JasonGross/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/HoTT/HoTT/labels/mathematical-question","name":"mathematical-question","color":"c7def8"}],"state":"closed","locked":false,"assignee":null,"milestone":null,"comments":1,"created_at":"2015-01-06T08:35:18Z","updated_at":"2015-01-06T22:01:34Z","closed_at":"2015-01-06T22:01:34Z","body":"I know that the following two theorems are true:\r\n```coq\r\nforall A P, Contr A -> Contr { x : A | P x } -> forall x, Contr (P x)\r\nforall A P, IsHProp A -> IsHProp { x : A | P x } -> forall x, IsHProp (P x)\r\nforall A P, IsHSet A -> IsHSet { x : A | P x } -> forall x, IsHSet (P x)\r\n```\r\nDoes this generalize?  Is there a proof of this somewhere in the library already?\r\n"}}