{"action":"created","issue":{"url":"https://api.github.com/repos/c-corn/corn/issues/37","repository_url":"https://api.github.com/repos/c-corn/corn","labels_url":"https://api.github.com/repos/c-corn/corn/issues/37/labels{/name}","comments_url":"https://api.github.com/repos/c-corn/corn/issues/37/comments","events_url":"https://api.github.com/repos/c-corn/corn/issues/37/events","html_url":"https://github.com/c-corn/corn/issues/37","id":190869823,"number":37,"title":"[math-classes] Additional axiom on inner product spaces: 0 = ⟨v,v⟩ iff v = mon_unit ","user":{"login":"siddharthist","id":4294323,"avatar_url":"https://avatars.githubusercontent.com/u/4294323?v=3","gravatar_id":"","url":"https://api.github.com/users/siddharthist","html_url":"https://github.com/siddharthist","followers_url":"https://api.github.com/users/siddharthist/followers","following_url":"https://api.github.com/users/siddharthist/following{/other_user}","gists_url":"https://api.github.com/users/siddharthist/gists{/gist_id}","starred_url":"https://api.github.com/users/siddharthist/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/siddharthist/subscriptions","organizations_url":"https://api.github.com/users/siddharthist/orgs","repos_url":"https://api.github.com/users/siddharthist/repos","events_url":"https://api.github.com/users/siddharthist/events{/privacy}","received_events_url":"https://api.github.com/users/siddharthist/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":1,"created_at":"2016-11-21T23:52:18Z","updated_at":"2016-11-22T09:49:50Z","closed_at":null,"body":"The [Wikipedia definition of an inner product space](https://en.wikipedia.org/wiki/Inner_product_space#Definition) has the following extra axiom: \r\n```coq\r\n0 = ⟨v,v⟩ <-> v = mon_unit \r\n```\r\nwhich isn't present in the current formalism. Should we rewrite the positivity rules as follows?\r\n```coq\r\n   ; in_pos_def1    :> ∀ v, PropHolds (0 ≤ ⟨v,v⟩)\r\n   ; in_pos_def2    :> ∀ v, 0 = ⟨v,v⟩ <-> v = mon_unit\r\n   }.\r\n```"},"comment":{"url":"https://api.github.com/repos/c-corn/corn/issues/comments/262194830","html_url":"https://github.com/c-corn/corn/issues/37#issuecomment-262194830","issue_url":"https://api.github.com/repos/c-corn/corn/issues/37","id":262194830,"user":{"login":"spitters","id":210638,"avatar_url":"https://avatars.githubusercontent.com/u/210638?v=3","gravatar_id":"","url":"https://api.github.com/users/spitters","html_url":"https://github.com/spitters","followers_url":"https://api.github.com/users/spitters/followers","following_url":"https://api.github.com/users/spitters/following{/other_user}","gists_url":"https://api.github.com/users/spitters/gists{/gist_id}","starred_url":"https://api.github.com/users/spitters/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/spitters/subscriptions","organizations_url":"https://api.github.com/users/spitters/orgs","repos_url":"https://api.github.com/users/spitters/repos","events_url":"https://api.github.com/users/spitters/events{/privacy}","received_events_url":"https://api.github.com/users/spitters/received_events","type":"User","site_admin":false},"created_at":"2016-11-22T09:49:50Z","updated_at":"2016-11-22T09:49:50Z","body":"Yes, well spotted. Also, it would be natural to make a normed space out of an inner product space."}}
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