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Questions tagged [isabelle]

Isabelle is a generic proof assistant, with Isabelle/HOL as main instance.

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Isabelle use Locale or Context outside of any locale

I have defined locale and proved a few theorems. Now I need to use them outside of this locale/context. How can I do so? Can I obtain theorem with hypotheses extended by locale's assumptions? (Like ...
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Is there a way to communicate with the Isabelle theorem prover through python?

I want to build a python API for Isabelle. I was wondering if it's possible? Is it possible to send proofs, tactics, command and all that jedit would be doing through Python and type check the proofs?
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Using an inverse value of an injective function

I'm trying to prove this lemma: lemma assumes "x = inv f y" and "inj f" and "x ≠ undefined" shows "y ∈ range f" using assms try But Nitpick tells me this statement is not true: Trying "...
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Can I change the notation in a built-in Isabelle type-class

I have made a type of mine an instance of monoid_add: instantiation "marking_ext" :: (monoid_add) monoid_add begin definition marking_add_def: "M + N = ... end I can now use the ...
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1answer
70 views

Isabelle resolves interpretation

I'm using Isabelle 2019 and got some troubles regarding locals: I'm constructing a locale with an abbrevation, e.g.: interpretation myInstance : myLocale "abbreviation" I'm using this with a ...
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Finding facts to match in Eisbach

I want to write an Eisbach method which pattern matches agains the facts reported by print_facts. However, I can't figure out the name of that (dynamic) set of facts. Example: proof { fix A B ...
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3answers
73 views

Why do we need to prove both proposition to apply Disjunction Elimination in Isabelle?

I was seeing the proof rule for disjunction elimination and I noticed we have to prove BOTH statements to use it: ?P ∨ ?Q ⟹ (?P ⟹ ?R) ⟹ (?Q ⟹ ?R) ⟹ ?R why is that? Like in normal logic if I knew ONE ...
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1answer
53 views

Is there a rewrite tactic in Isabelle?

For example in Coq there is rewrite and we can also put arrows `<-: Inductive bool: Set := | true | false. Lemma equality_of_functions_commutes: forall (f: bool->bool) x y, (f x) = (...
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1answer
40 views

Preimage of a function in Isabelle

I made this: abbreviation "preimage f y ≡ { x . f x = y }" Isn't there a built-in definition I could be using instead? How would I find that?
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30 views

Cases with custom rule in Eisbach

I wrote this rule: method rule_inversion uses P = (cases rule: nt_network[OF P]) but Isabelle tells me Rule has fewer premises than arguments given The exact nt_network doesn't seem to matter, ...
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1answer
33 views

How does one toggle auto update in Isabelle with a keyboard shortcut?

I wanted to stop isabelle from doing the proof steps as I write since its impossible to remember complicated equations as I try to tell it with rule_tac what the term should be while it dissapears. ...
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1answer
34 views

Generalize a claim in a structural induction proof to be able to use the induction hypothesis

I want to prove the following lemma fixes pi :: "'a path" and T :: "'a ts" shows "valid_path T pi s ⟹ ∀ op ∈ set pi. valid_operator T op" by induction on pi where fun valid_path :: "'a ts ⇒ 'a ...
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Case analysis on function definition in Isabelle

Imagine I have a function definition with three cases: function f where eq1 if cond1 | eq2 if cond2 | eq3 if cond3 How can I prove some equation: f x y = f y x using case analysis on the ...
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1answer
66 views

How to apply standard to all subgoals in Isabelle?

To prove an equality "A = B" one can prove two inclusions "A ⊆ B" and "B ⊆ A". Now, I'm using the method "standard" to transform this goal into the goal "fix x in A and show x is in B". However, I don'...
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Using the type-to-sets approach for defining quotients

Isabelle has some automation for quotient reasoning through the quotient package. I would like to see if that automation is of any use for my example. The relevant definitions is: definition e_proj ...

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