# [isabelle] rule is sometimes very slow

Hi,
consider the following theory:
theory Scratch imports Main
begin
abbreviation funswapid :: "'a ⇒ 'a ⇒ 'a ⇒ 'a" (infix "⇌⇩F" 90) where
"x ⇌⇩F y ≡ Fun.swap x y id"
notepad begin
fix uv uw vu vw wu wv f GM HM m n a
assume "(vw ⇌⇩F vu ∘ f HM ^^ Suc m ∘ (uw ⇌⇩F uv ∘ vw ⇌⇩F vu)) a = (f
GM ^^ Suc n) a"
then have "∃m. (vw ⇌⇩F vu ∘ f HM ^^ Suc m ∘ (uw ⇌⇩F uv ∘ vw ⇌⇩F vu)) a
= (f GM ^^ Suc n) a"
by (rule exI)
end
The proof step "rule exI" takes several seconds to complete on my
machine (in Isabelle 2014). Similar proofs, like
by (rule_tac exI)
by - (rule exI)
by - (erule exI)
by metis
by blast
are instantaneous, as expected. I looked a bit into the implementation
of rule and it seems that most time is spend
in evaluating the result of
Drule.multi_resolves facts @{thms exI}
-- Lars

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