Re: [isabelle] Rewrites for a sublocale with UNIV as the carrier set



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




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