Using Ogden’s Lemma versus regular Pumping Lemma for ContextFree Grammars
By : Illya Shykyrinsky
Date : March 29 2020, 07:55 AM
hop of those help? One important stumbling issue here is that "being able to pump" does not imply context free, rather "not being able to pump" shows it is not context free. Similarly, being grey does not imply you're an elephant, but being an elephant does imply you're grey... code :
Grammar context free => Pumping Lemma is definitely satisfied
Grammar not context free => Pumping Lemma *may* be satisfied
Pumping Lemma satisfied => Grammar *may* be context free
Pumping Lemma not satisfied => Grammar definitely not context free
# (we can write exactly the same for Ogden's Lemma)
# Here "=>" should be read as implies

how to make an example to test the rev_app immediately after lemma proved. an starting example for custom lemma
By : user3630847
Date : March 29 2020, 07:55 AM

how to discover new lemma or guess or search the next lemma which want to be proved in Isabelle
By : user3724273
Date : March 29 2020, 07:55 AM
will be helpful for those in need Johansson et al. have recently presented a system for theory exploration, that is, coming up with lemmas based on your definitions. You can find their implementation on GitHub and the paper on arXiv. In the paper, you will also find a lot of examples. The only drawback is that, as far as I can tell, their implementation only works with Isabelle20132. Johansson, Moa, et al. "Hipster: Integrating Theory Exploration in a Proof Assistant." Intelligent Computer Mathematics. Springer International Publishing, 2014. 108122.

Isabelle auto prover works on lemma, hangs on special case of the lemma
By : Paweł Kaczorowski
Date : March 29 2020, 07:55 AM
will be helpful for those in need First of all: it is inconvenient to state goals with the HOL universal quantifier ∀. Free variables in goals are implicitly universally quantified anyway, so you can simply leave out the ∀. You will, however, tell the induction command to universally quantify these variables in the induction step using arbitrary: code :
lemma ListSumTAux_1 : "ListSumTAux xs (a+b) = a + ListSumTAux xs b"
apply (induct xs arbitrary: a b)
apply (auto)
done
⋀a. ListSumTAux xs a = a + ListSumTAux xs 0
ListSumTAux xs a → a + ListSumTAux xs 0 → a + (0 + ListSumTAux xs 0) →
a + (0 + (0 + ListSumTAux xs 0))

Use of Handshaking Lemma to find number of subarrays with even Sum
By : Greg McClement
Date : March 29 2020, 07:55 AM
fixed the issue. Will look into that further I was attempting to do practice questions and came across a solution I do not understand the reasoning behind. , First we have an array of numbers, for example: code :
[1,3,5,2,10,7]
[1,4,9,11,21,28]
2*E = odd*(odd  1) + even*(even  1) => E = odd*(odd  1)/ 2 + even*(even  1)/2

