*To*: Johannes HÃlzl <hoelzl at in.tum.de>, <cl-isabelle-users at lists.cam.ac.uk>*Subject*: Re: [isabelle] Monotonicity of rtrancl for inductive/inductive_set*From*: Andreas Lochbihler <andreas.lochbihler at inf.ethz.ch>*Date*: Tue, 7 Jul 2015 17:36:33 +0200*In-reply-to*: <1436283199.2348.7.camel@in.tum.de>*References*: <559B4E19.2080302@nicta.com.au> <1436283199.2348.7.camel@in.tum.de>*User-agent*: Mozilla/5.0 (X11; Linux x86_64; rv:31.0) Gecko/20100101 Thunderbird/31.7.0

Hi Johannes,

Best, Andreas On 07/07/15 17:33, Johannes HÃlzl wrote:

So, you are proposing that this rule should be added to the Isabelle repository as default rule? Sure I can add this rule! But I wonder where the HOL implication â comes from? Is it introduced by the inductive package? - Johannes Am Dienstag, den 07.07.2015, 13:57 +1000 schrieb Thomas Sewell:Hello Isabelle users. It looks like the following inductive-compatible monotonicity rule for rtranclp is useful for some inductive definitions. lemma rtrancl_mono_proof[mono]: "(âa b. x a b â y a b) â rtranclp x a b â rtranclp y a b" apply (rule impI, rotate_tac, induct rule: rtranclp.induct) apply simp_all apply (metis rtranclp.intros) done It looks like this is the kind of rule the system should supply by default, especially as coercion between trancl/rtrancl can leave users quite confused what the problem really is. Cheers, Thomas.

**Follow-Ups**:**Re: [isabelle] Monotonicity of rtrancl for inductive/inductive_set***From:*Johannes Hölzl

**References**:**[isabelle] Monotonicity of rtrancl for inductive/inductive_set***From:*Thomas Sewell

**Re: [isabelle] Monotonicity of rtrancl for inductive/inductive_set***From:*Johannes Hölzl

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