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



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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