*To*: cl-isabelle-users at lists.cam.ac.uk*Subject*: Re: [isabelle] Rewrites for a sublocale with UNIV as the carrier set*From*: Lukas Stevens <lukas.stevens+isabelle-users at in.tum.de>*Date*: Mon, 8 Feb 2021 11:49:40 +0100*In-reply-to*: <3b568042-7a61-b36a-aeca-8cebe1babe9f@trs.cm.is.nagoya-u.ac.jp>*References*: <4f696043-2b46-d647-7f67-74f23957acf8@in.tum.de> <3b568042-7a61-b36a-aeca-8cebe1babe9f@trs.cm.is.nagoya-u.ac.jp>*User-agent*: Mozilla/5.0 (X11; Linux x86_64; rv:78.0) Gecko/20100101 Thunderbird/78.6.1

That does not seem to work. See the example below:

theory Scratch imports Main begin axiomatization P :: "'a ⇒ bool" axiomatization Z :: "'a ⇒ bool" locale foo = fixes A :: "'a set" begin lemma bar: "X ⊆ A ⟹ Z A ⟹ P X" sorry end locale bar begin sublocale foo UNIV rewrites "Y ⊆ UNIV ≡ True" and "⋀Q. (True ⟹ PROP Q) ≡ Q" and "⋀Q. (True ⟹ Q) ≡ Trueprop Q" by auto (* ⟦True; Z UNIV⟧ ⟹ P ?X instead of Z UNIV ⟹ P ?X *) thm bar end end

On 2/7/21 3:37 AM, YAMADA, Akihisa
wrote:

Hello Lukas,

I had the same question before but it was not concluded. As a workaround, I'm declaring the two rewrites and it works for any number of assumptions.

"⋀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 holds on a carrier set A. Often, one wants to specialise this to a locale foo where A is the UNIV. The problem is that theorems in foo_on often have assumptions of the form "X ⊆ A" which are "X ⊆ UNIV" in the context of foo. Those assumptions are trivial so I want to get rid of them using rewrites 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

**Follow-Ups**:**Re: [isabelle] Rewrites for a sublocale with UNIV as the carrier set***From:*YAMADA, Akihisa

**References**:**[isabelle] Rewrites for a sublocale with UNIV as the carrier set***From:*Lukas Stevens

**Re: [isabelle] Rewrites for a sublocale with UNIV as the carrier set***From:*YAMADA, Akihisa

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