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Questions tagged [isar]

Intelligible semi-automated reasoning (Isar) is an approach to human readable formal proof documents (as opposed to state-based scripting).

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Recall Isabelle's "Go to the definition" command. (Isar, JEdit)

There exists a shortcut or command which allows one to go straight to the definition of symbol or lemma. (Like "ALT+," in GTAGS for Emacs) It is quite handy contrary (just imho) to the Coq's one, where one have to do Search command in an IDE. I…
ged
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How to pass assumptions to interpretation of locale

I would like to use some properties of my structure in the proof required by a locale interpretation As an example, suppose I defined the predicate P and proved some lemmas (add is a closed binary operation, add is associative and there exists zero…
edoput
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Isar proof of conjunction

I'm trying to prove something using Isar; so far, I've gotten to a goal that looks like this: (∀P Q. P ≠ Q ⟶ (∃!l. plmeets P l ∧ plmeets Q l)) ∧ (∀P l. ¬ plmeets P l ⟶ (∃!m. affine_plane_data.parallel plmeets l m ∧ plmeets P m)) ∧ (∃P Q. P ≠ Q ∧…
John
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Access elements of data types

Is it possible in Isabelle to access the individual elements of a data type? Let's say I have the following data type: datatype foo = mat int int int int and (e.g. in a lemma) fixes A :: foo Is it possible to access the single elements of A? Or…
Benedikt
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How can I prove the lemma in Exercise 4.6 in “Programming and Proving in Isabelle/HOL”?

I am trying to solve Exercise 4.6 in “Programming and Proving in Isabelle/HOL”. It asks to define a function elems :: "'a list ⇒ 'a set" that converts a list into a set, and to prove the lemma "x ∈ elems xs ⟹ ∃ ys zs . xs = ys @ x # zs ∧ x ∉ elems…
Wolfgang Jeltsch
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How can I efficiently prove existential propositions with multiple variables in Isabelle/Isar?

Say I want to prove the lemma ∃ n m k . [n, m, k] = [2, 3, 5] in Isabelle/Isar. If I go ahead as suggested in the Isabelle/HOL tutorial on page 45, my proof looks as follows: lemma "∃ n m k . [n, m, k] = [2, 3, 5]" proof show "∃ m k . [2, m, k] =…
Wolfgang Jeltsch
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Reordering goals (Isabelle)

I would like to know how to reorder goals in the following situation: lemma "P=Q" proof (rule iffI, (*here I would like to swap goal order*), rule ccontr) oops I would like a solution that doesn't involve changing the lemma statement. I realise…
IIM
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Proof by induction with three base cases (Isabelle)

I want to be able to prove a statement by induction on n (of type nat). It consists of a conditional whose antecedent is only true for n >= 2. A conditional whose antecedent is false is always true. So I'd like to prove the cases n=0, n=1 and n=2…
IIM
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Intro rule for "∀r>0" in Isabelle

When I have a goal such as "∀x. P x" in Isabelle, I know that I can write show "∀x. P x" proof (rule allI) However, when the goal is "∀x>0. P x", I cannot do that. Is there a similar rule/method that I can use after proof in order to simplify my…
IIM
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Sledgehammer gives insufficient proof tactic

I have theory Even imports Main begin inductive structural_even :: "nat ⇒ bool" where "structural_even 0" | "structural_even n ⟹ structural_even (Suc(Suc n))" fun computational_even :: "nat ⇒ bool" where "computational_even 0 = True" |…
Gergely
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Defining a quotient_type in Isabelle

I'm still trying to reason over semantic equality in Isabelle. I want to compare two formula and see whether they are equal. I've been told before, that i need quotienttypes for this. So i tried to define myself a quotiernttype, but apperently my…
TKler
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Proving a simple arithmetic statement with rewriting in Isabelle

I am trying to prove a big case distinction in Isabelle for some (conceptually) simple arithmetic statement. During the proof, I stumbled upon the following subgoal. ⋀d l k. 0 < d ⟹ ¬ 2 * k + 1 ≤ 2 * l ⟹ 2 * l ≠ 1 ⟹ - (2 * l) < 2…
HdM
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Defining disjoint union of different types in Isabelle and more

I asked a series of question to get to the point I can define the following simple model in Isabelle, But I still stuck in getting what I wanted. I try to very briefly describe the problem with an example: Example: Suppose I have two classes Person…
qartal
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Case names for locale interpretation

Some of my locals have quite a few assumptions, very much resembling inductions over data types (that’s where the assumptions come from). When interpreting such a locale, having named cases would be very handy. How do I achieve that the following…
Joachim Breitner
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How to use obtain in existential proofs?

I tried to prove an existential theorem lemma "∃ x. x * (t :: nat) = t" proof obtain y where "y * t = t" by (auto) but I could not finish the proof. So I have the necessary y but how can I feed it into the original goal?
Gergely
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