Re: [isabelle] case rule and OF



Dear Esseger,

When you instantiate some premises of a rule with OF, all the case name information gets erased (because it is not trivial to determine how they would have to be shifted). However, you normally do not instantiate premises manually in case distinctions, but appropriately declare the first n premises to be unified with the facts chained in using the "consumes n" attribute. "lemma assumes ... obtains ..." implicitly sets "consumes" appropriately. Hence, you merely have to chain in the necessary assumptions, as I had shown in my example.

Andreas

On 21/09/16 09:01, Esseger wrote:
Thanks for your answer, and sorry for my typo: I indeed meant

proof (cases rule: my_case_rule[OF `p â  1`])

With this construction, the case names are not honored (while the construction you advocate

using `p >= 1` proof (cases rule: my_case_rule)

works fine)

Best,
Esseger


Le 21/09/2016 Ã 08:23, Andreas Lochbihler a Ãcrit :
Dear Esseger,

Case names as specified for rules are only honored by the proof methods "cases",
"induct" and "coinduct" (and their derivatives "induction" and "coinduction"), but not
plain "rule". Your rule "my_case_rule" should work if you use "cases" (which is the
appropriate method here, because you are doing a case distinction). So, the following
should do the job:

lemma
  assumes "p â (1::ennreal)"
  show foo
  using `p >= 1`
proof (cases rule: my_case_rule)

Hope this helps,
Andreas

On 20/09/16 23:17, Esseger wrote:
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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