Intelligible semi-automated reasoning (Isar) is an approach to human readable formal proof documents (as opposed to state-based scripting).
Questions tagged [isar]
95 questions
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Why can't I simplify Σ {0} = 0 in Isabelle to make them equal?
I was going through chapter 5 (Isar) and I tried doing the structural induction proof for "Σ{0..n::nat} = n*(n+1) div 2" but it fails:
lemma "Σ{0..n::nat} = n*(n+1) div 2"
proof (induction n)
show "Σ{0..0::nat} = 0*(0+1) div 2" by simp
next
fix…
Charlie Parker
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Isabelle : Choose assumption / Choose Goal / Specify metavariable
1)How to choose assumption that I want to apply in Isabelle/FOL theorem?
There is a case of proof, where I cannot use "apply assumption".
axiomatization
where aax8 : ‹(A-->C)-->(B-->C)-->(A∨B-->C)›
and aax11 : "A∨~A"
lemma ewfw : ‹…
ged
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Isabelle FOL partial Rule application
Let's assume we have such variant of Modus Ponens
lemma invDed: ‹(A-->B)==>(A==>B)›
apply(rule mp)
apply assumption
apply assumption
done
Can it be applied for proving the theorem? (I mean A:=A, B:=A, and A-->A we use as if it was…
ged
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Isabelle/HOL/Isar: How do I make formulas like "∃(x::nat). (x ≠ 2 ∧ (x ≠ 2 ⟶ x = 1))" easier to prove?
My story is quite long, and my code for what I actually wanted to do is also quite long. So first I will describe what I have tried with the formula in the title, and then I will describe how I encountered something like this in practice, putting my…
Imperishable Night
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Basic Isabelle/Isar style (exercise 4.6)
I'm interested in using Isabelle/Isar for writing proofs which are both human-readable and machine checked, and I am looking to improve my style and streamline my proofs.
prog-prove has the following exercise:
Exercise 4.6. Define a recursive…
Nick Hu
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Instantiating a class from a concrete object?
I'm attempting to formalize a series of proofs about topology from a book [1] in Isabelle.
I want to encode the idea that a topological space (X,T) consists of a set X of "points" (elements of some arbitrary type 'a), and a set of subsets of X,…
tangentstorm
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How do I refer to the current subgoal in Isar?
I am trying to solve Exercise 4.7 from Programming and Proving in Isabelle.
I run into a case where I have proved False and therefore everything, but I cannot close the case because I do not know how to refer to my proof obligation.
theory…
rosento
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Why won't the 'linordered_field_class.frac_le' rule work? (Isabelle)
I am trying to use the rule linordered_field_class.frac_le in an Isar proof. Here is the code snippet (it may depend on the previous parts of the proof, but that is unlikely). n is of type nat.
...
then have 4:"2 ≤ (2^(n+1)::real)" by simp
…
IIM
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Create a quotient-lifted type with polymorphism over working set and equivalence relation in Isabelle/HOL
I would like to create a quotient type with quotient_type in Isabelle/HOL in which I would left "non-constructed" the non-empty set S and the equivalence relation ≡. The goal is for me to derive generic properties w.r.t. S and ≡ over the…
Hai Nguyen Van
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How to define Subtypes in Isabelle and what they mean?
The question regarding subtyping in Isabelle is very lengthy here. So my simple question is that how I can define type B to be a subtype of A if I define A as below:
typedecl A
By doing this I would like to make all operations and relations…
qartal
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Untyped set operations in Isabelle
I have the following code in Isabelle:
typedecl type1
typedecl type2
consts
A::"type1 set"
B::"type2 set"
When I want to use union operation with A and B as bellow:
axiomatization where
c0: "A ∩ B = {}"
Since A and B are sets of different…
qartal
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How type casting is possible in isabelle
Supose I have the following code in Isabelle:
typedecl type1
typedecl type2
typedecl type3
consts
A::"type1 set"
B::"type2 set"
When I want to use union operation with A and B as bellow:
axiomatization where
c0: "A ∪ B = {}"
Since A and B…
qartal
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2 answers
Factoring out a lemma premise as a definition causes failure in proof method (auto) application in isabelle
I have the following code in Isabelle:
typedecl Person
consts age :: "Person ⇒ int"
lemma "⟦(∀p::Person. age p > 20);p ∈ Person⟧⟹ age p > 20"
apply (auto)
done
The auto proof method works fine and proves the lemma! when I want to factor out the…
qartal
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Organizing constraints in isabelle in order to model a system
Suppose that I have the following expression in Isabelle/HOL:
typedecl Person
typedecl Car
consts age :: "Person ⇒ int"
consts drives ::"(Person × Car) set"
consts owns ::"(Person × Car) set"
This is supposed to model Person and Car types with…
qartal
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Can I "map" an "OF" over a list of lemmas
I just wrote this code:
lemmas gc_step_intros =
normal[OF step.intros(1)] normal[OF step.intros(2)] normal[OF step.intros(3)]
normal[OF step.intros(4)] normal[OF step.intros(5)] drop
where step.intros really only has 5 lemmas. Is there a…
Joachim Breitner
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