[isabelle] case rule and OF



Dear all,

I am trying to set a convenient case rule, to distinguish if, given a parameter p â 1 in ennreal, it is equal to 1, or between 1 and infinity, or infinite. When it is strictly between 1 and infinity, I would also like p to be written as p = ennreal p2, for some real number p2.

I would like to use it as:

lemma
  assumes "p â (1::ennreal)"
  show foo
proof (rule my_case_rule[OF `p â 1`])
  case one
  then show ?thesis sorry
next
  case (gr p2)
  then show ?thesis sorry
next
  case PInf
  then show ?thesis sorry
qed

I tried to define my rule as:

lemma my_case_rule:
  assumes "p â (1::ennreal)"
  obtains (gr) p2 where "p = ennreal p2" "p2 > 1"
    | (one) "p = 1"
    | (PInf) "p = â"
using assms by (metis (full_types) antisym_conv ennreal_cases ennreal_le_1 infinity_ennreal_def not_le)

It doesn't work, as the names of the cases are not respected, replacing them with the names 1, 2, 3 (with which I can write the proofs, for sure, but this is much harder to read).

I tried several modifications of the rule to keep the names, with modifiers such as case_names or consumes, to no avail. I could not locate in the reference manual any hint on the canonical way to write this kind of thing. Any help on the best practice in this situation?

Best,
Esseger






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