*To*: lukas.stevens+isabelle-users at in.tum.de, isabelle-users at cl.cam.ac.uk*Subject*: Re: [isabelle] Rewrites for a sublocale with UNIV as the carrier set*From*: "YAMADA, Akihisa" <ayamada at trs.cm.is.nagoya-u.ac.jp>*Date*: Sun, 7 Feb 2021 11:37:23 +0900*In-reply-to*: <4f696043-2b46-d647-7f67-74f23957acf8@in.tum.de>*References*: <4f696043-2b46-d647-7f67-74f23957acf8@in.tum.de>*User-agent*: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.7.0

Hello Lukas,

"⋀Q. (True ⟹ PROP Q) ≡ Q" and "⋀Q. (True ⟹ Q) ≡ Trueprop Q" Best regards, Akihisa On 2021/02/05 22:15, Lukas Stevens wrote:

Hello,suppose I have a locale foo_on that assumes that some predicate P holdson a carrier set A. Often, one wants to specialise this to a locale foowhere A is the UNIV. The problem is that theorems in foo_on often haveassumptions of the form "X ⊆ A" which are "X ⊆ UNIV" in the context offoo. Those assumptions are trivial so I want to get rid of them usingrewrites but this doesn't seem to work as the example below shows:axiomatization P :: "'a ⇒ bool" locale foo = fixes A :: "'a set" begin lemma bar: "X ⊆ A ⟹ P X" sorry end locale bar begin (* (True ==> Q) ≡ Trueprop Q works for the theorem bar but not for theorems with multiple assumptions. *) sublocale foo UNIV rewrites "Y ⊆ UNIV ≡ True" and "(True ⟹ PROP Q) ≡ PROP Q" by auto end What is going wrong here? Cheers, Lukas

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