This site is intended to help getting started with using Isabelle/HOL and the Isabelle jEdit editor. This page in particular is the quick cheat sheet and can be used as a reference.
Please use the FAQ  Ask Questions page to post and view questions and the Exam Questions page to collect possible questions for the exams. The Goals of the Exercises page summarizes what you should have learned by doing them.
For best practices in Isabelle/HOL, see the corresponding page.
Please also check out and add stuff concerning the Editor, Isabelle/HOL Syntax and useful External References. Last but not least, you can post and check out Example Code.
Help us to improve the Wiki by checking and complementing existing content, as well as creating wanted pages!
You can download and install Isabelle from http://isabelle.in.tum.de/. To run Isabelle you can run `isabelle jedit m brackets`.
Isabelle is already installed on the SCI machines tux1, tux2, tux3 and tux9. On those machines you can start it by simply typing `isabelle` into a terminal.
Every Isabelle/HOL theory looks like this:
theory MyTheory imports Main begin ... end
It is important that the name of the theory is equal to the name of the file.
Isabelle uses many symbols which are not available on a normal keyboard. You can either use the “Symbols” tab in jedit or type the following shortcuts and use autocomplete with “TAB” to get the correct symbol.
Logics  

type  /\ or &  \/ or   \not or ~  >  <>  \forall or !  \exists or ? 
Meta  

type  !!  ==>  ==  [  ] 
Math  

type  =  ~=  <  >  ⇐  >= 
Sets  

type  \in or :  \notin or ~:  \subset  \subseteq  \inter  \union 
If you know LaTeX, try using commands you know from there.
Heuristic: try ML! Major differences:
primrec
, fun
and function
#
, not ::
.definition $ident where “$ident == $expression”
– assigns the value of $expression
to identifier $ident
lemma ($name :)? “$formula”
– states $formula
as lemma, assigns it a name (if given) and creates a proof goaltheorem ($name :)? “$formula”
– states $formula
as theorem, assigns it a name (if given) and creates a proof goaldatatype
type_synonym
primrec
– used for primitive recursive functions (nothing to prove, but heavy constraints)fun
– used for more general functions, but have to prove termination (e.g. via wellfounded order)function
– used for arbitrary function definitions; have to prove all kinds of stuff
Apply method $method
with parameters $params
by entering apply ($method $params)
. If you have no parameters, you can just write apply $method
. For example, a (very simple) proof can look like this:
lemma "[ A; A > B ] ==> B" apply (frule mp) apply assumption+ done
Name  Parameters  All goals  Safe  New Goals  Variants 

assumption  —  x  
cases  an expression  x  x  case_tac 

drule  a rule  x  drule(k) , drule_tac 

erule  a rule  x  erule(k) , erule_tac 

fold  a definition (or equation)  x  x  
frule  a rule  x  x  frule(k) , frule_tac 

induct  a variable  x  induct_tac 

insert  a theorem  x  x  cut_tac 

rename_tac  list of identifiers  
rotate_tac  an integer  x  
rule  a rule  x  rule(k) , rule_tac 

split  a splitting rule  ?  x  
subgoal_tac  a formula  x  
subst  a definition (or equation)  x  x  subst (asm) 

thin_tac  a formula  
unfold  a definition (or equation)  x  x  ? 
Name  Classical  Simp  All goals  Safe  Splits  Finishes  Strength  Weakness 

arith  x  x  linear arithmetics  exponentially slow for many operators  
auto  x  x  x  x  
blast  x  x  x  logics, sets; fast  
clarify  x  x  
clarsimp  x  x  x  
force  x  x  x  x  
metis  x  x  x  logics  no sets  
safe  x  x  x  x  
simp  x  x  x  
simp_all  x  x  x  x 
Note that safety of automated proof methods can be sabotaged by adding unsafe rules to rule sets used.
There are many more methods. You can print them by issuing the command print_methods
, key combination Cc Ca h m
or via [Isabelle → Show Me → Methods].
Symbol  Semantics  Example 

+  Applies the method as often as applicable, but at least once.  assumption+ 
(_,_)  Applies all the methods in sequence and fails if any one is not applicable.  (rule mp, simp) 
[n]  Applies the method only to the first n subgoals.  auto[5] 
The sequencing of methods has the additional effect that backtracking is used to make the whole sequence work. As many methods could be applied in different ways, e.g. by matching the premise with a different assumption, failure of one step of the sequence just leads to trying another possibility for one of the steps before.
Attributes (also: directives) can be used to obtain new, more specific theorems from already proven, more general ones. In other words, they allow you to adapt theorems to your current needs. There are two major uses:
$thm [$attr1, $attr2, …]
– can be used in any place where you would put a theorem or rule. Instead of $thm
itself, the result of applying the given attributes from left to right is used.lemmas $name = $thm [$attr1, $attr2, …]
– assigns a new name to the modified theorem, enabling later (re)use.(lemmatheorem) $name [$attr1, $attr2, …] : $formula
– applies the given attributes from left to right after the proof is finished, assigning the result to the given name.Attribute  Semantics 

of $t1 $t2 …  Replaces variables with the given terms in order. Use _ for keeping the variable. (Example) 
where $v1=$t1 and $v2=$t2 …  Replaces the specified variables in a theorem with the given terms. (Example) 
THEN $rule  Applies the given rule to a theorem and returns the conclusion. (Example) 
OF $thm1 $thm2  Generates a new instance of a rule using the given theorems. (Example) 
simplified  Applies simp to a theorem and returns the result. (Example) 
rotated $k  Rotates the given theorem's assumptions by $k to the left. If no value is given, $k=1 is assumed. (Example) 
symmetric  Equivalent to THEN sym . (Example) 
Other attributes perform some action with a theorem. They probably only make sense in lemma/theorem definitions or together with lemmas
(see above):
Attribute  Action 

iff  Enables both simplifier and classical reasoner to use this theorem. Only use with equivalences whose righthand side is “simpler” than lefthand side. 
rule_format  Lifts a toplevel implication into Pure logic, i.e. enables reasoners to use the theorem as rule. 
simp  Allows the simplifier to use this theorem. 
There are many more attributes. You can print them by issuing the command print_attributes
, key combination Cc Ca h a
or via [Isabelle → Show Me → Attributes].
Command  Semantics 

done  finishes the proof if no more subgoals left 
by $method  tries to finish the rest of the proof with the given method followed by assumption+ 
sorry  forces an unfinished proof to be considered successful (i.e. lemma/theorem is usable!) 
oops  aborts the proof and drops the lemma/theorem 
conjI
, conjE
, conjunct1
, conjunct2
disjI1
, disjI2
, disjE
impI
, impE
, mp
iffI
, iffE
allI
, spec
, bspec
exI
, exE
, bexI
notI
, notE
FalseE
classical
contrapos_(ppnppnnn)
thm $name
– command that shows theorem with name $name
value $expr
– command that evaluates the specified expression and prints the resultprefer $k
– command that moves subgoal number $k
to the top of the listdefer
– command that moves the current subgoal to the bottom of the list quickcheck
– command that tries to find a counterexample to the current subgoal. Useful to check wether an unsafe rule did harm. Note: it might not find a counterexample even if the goal can not be proven!refute
and nitpick
– similar to quickcheck but try to find counterexample models, not only variable assignments. Can handle more constructs.sledgehammer
– command that invokes fully automated theorem provers both locally and on remote clusters. Tries to find a (minimal) set of theorems needed to solve the current goal.lfp $function
– a function that yields the least fixpoint of the given functionundefined
– a distinguished value for any typef(x := y)
– the function update: the result of this expression is the function f
updated such that it now returns y
for parameter x
; the other values do not change.{x. P x}
– the set of values fulfilling predicate P
. For instance, {x::nat. x dvd 125}
is the set of (natural) divisors of .{E x  x. P x}
– the set of values created by expression E
, for all values fulfilling predicate P
, {x + y  x y. x < 10 /\ y < 10}
is the set of sums of all pairs of natural numbers with a single digit.