[isabelle] Fw: Problems with `drule` and `erule` in the presence of chained facts



Oops, only sent that privately


-------- Original Message --------
Subject: Re: [isabelle] Problems with `drule` and `erule` in the presence of chained facts
From: lammich at in.tum.de
To: Wolfgang Jeltsch <wolfgang-it at jeltsch.info>
CC:


Hi

This is a well known idiosyncrasy of Isabelle: chained facts are treated specifically by some methods. You can use apply - to online all chained facts. An alternative workaround that is commonly used, but not considered good style by some people, is to use the _tac versions, eg drule_tac, erule_tac and rule_tac. This will also inline chained facts.

Peter


-------- Original Message --------
Subject: [isabelle] Problems with `drule` and `erule` in the presence of chained facts
From: Wolfgang Jeltsch <wolfgang-it at jeltsch.info>
To: isabelle-users at cl.cam.ac.uk
CC:


Hi!

I’m developing a proof method that involves applications of `drule`.
This proof methods doesn’t work in the presence of chained facts,
because its `drule` invocations fail in this situation.

Consider the following minimal example code:

lemma "P ∧ Q ⟹ R"
apply (drule conjunct1)
oops

The invocation of `drule` correctly turns the goal into `P ⟹ R`.
However, it fails in the following situation:

lemma "P ∧ Q ⟹ R"
using TrueI
apply (drule conjunct1)
oops

Why is that, and how can `drule` been made work also in the presence of
chained facts?

I also tried to use `erule` instead of `drule`, but the same problem
occurred with that.

In my use case, I actually want to turn all chained facts into goal
premises anyhow. I can add the chained facts to the list of goal
premises by invoking `insert method_facts`, but this leaves the chained
facts in place, so that the problem with `drule` remains. Is there
perhaps a proof method that removes all chained facts?

I know that `simp` turns chained facts into goal premises. Therefore, my
current workaround is to invoke `simp` in a way where it essentially
doesn’t rewrite anything but only moves chained facts into the goal. To
this end, I’m using `(insert TrueI, simp only: True_implies_equals)`. This has the side effect of removing all previously existing
`True` premises, but this isn’t a problem in my use case. Still, I’d be
happy to use a cleaner solution.

All the best,
Wolfgang




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