Pattern: AdjectiveNamespaceDocumentationAdjective is a possibly negated (and paramaterized) attribute
Optionally the article id (aid) and order in article (absnr)
can be given. If available, presentational info
(number of the Pattern) is given in pid. The heuristic for
for displaying clusters is that attributes without pid have been
added automatically by cluster mechanisms.
The attribute kind (kind) 'V' can be added explicitly. Content Model
Adjective
Pattern: And
Pattern: AndNamespaceDocumentationConjunctive formula.
If available, presentational info is given in pid.Content Model
And
Pattern: ArgTypes
Pattern: ArgTypesNamespaceDocumentationArgument types of constructors, patterns, clusters, etc.Content Model
ArgTypes
Pattern: Article
Pattern: ArticleNamespaceDocumentationThe complete article after analyzer.
aid specifies its name in uppercase, and mizfiles
optionally gives a location of the local MIZFILES directory used
during processing the article (needed to know for browsing of
locally installed html in MIZFILES/html).Content Model
Article
Pattern: ArticleID
Pattern: ArticleIDNamespaceDocumentationThis is now only the unique name of an article.Content Model
ArticleID
Pattern: Assume
Pattern: AssumeNamespaceDocumentationOne assumption may consist of several propositions.Content Model
Assume
Pattern: AuxiliaryItem
Pattern: AuxiliaryItemNamespaceDocumentationAuxiliary items are items which do not change thesis.Content Model
(
%JustifiedProposition; | %Consider; | %Set; | %Reconsider; | %DefFunc; | %DefPred;
)
Pattern: BlockThesis
Pattern: BlockThesisNamespaceDocumentationThe block thesis is printed for proofs in the beginning and
for diffuse reasoning in the end.
For diffuse reasoning, the series of temporary subthesis corresponding to
all skeleton items is printed before the main theses (in the same order
as the skeleton items in the block). Content Model
BlockThesis
Pattern: By
Pattern: ByNamespaceDocumentationBy encodes one simple justification.Content Model
By
Pattern: ByExplanations
Pattern: ByExplanationsNamespaceDocumentationReports from the Mizar checker, now only arithmetical evaluations.
They are now only available when the verifier is compiled with a special
directive - this should be changed to a user option eventually. Content Model
ByExplanations
Pattern: CCluster
Pattern: CClusterNamespaceDocumentationConditional cluster.
This says that Typ with the first cluster has also the second
(optionally followed by its extended version created by rounding
up in current environment).
Optionally the article id (aid) and order in article (nr)
can be given.Content Model
CCluster
Pattern: Canceled
Pattern: CanceledNamespaceDocumentationCanceled theorem ( if on top-level), definition or registration
(if inside such blocks). We should add to this the number
of canceled items as an attribute.Content Model
Canceled
Pattern: Case
Pattern: CaseNamespaceDocumentationCase of one or more propositions.Content Model
Case
Pattern: CaseBlock
Pattern: CaseBlockNamespaceDocumentationBlock starting with one case, the direct and diffuse version
(this depends on the kind of its parent block).
The block thesis is printed for proofs in the beginning and
for diffuse reasoning in the end.Content Model
CaseBlock
Pattern: Choice
Pattern: ChoiceNamespaceDocumentationChoice term is defined by the type of its argument,Content Model
Choice
Pattern: Cluster
Pattern: ClusterNamespaceDocumentationCluster of adjectivesContent Model
Cluster
Pattern: Coherence
Pattern: CoherenceNamespaceDocumentationNo documentation available.Content Model
Coherence
Pattern: Compatibility
Pattern: CompatibilityNamespaceDocumentationNo documentation available.Content Model
Compatibility
Pattern: ComplexNr
Pattern: ComplexNrNamespaceDocumentationComplex rational numbers used in MizarContent Model
ComplexNr
Pattern: Conclusion
Pattern: ConclusionNamespaceDocumentationJustified conclusion. In text, this can appear as _hence_,
_thus_ or _hereby_ (which starts diffuse conclusion).Content Model
Conclusion
Pattern: Consider
Pattern: ConsiderNamespaceDocumentationFirst comes the reconstructed existential statement
and its justification, then the new local constants
and zero or more propositions about them.
For easier presentation, nr optionally contains the number
of the first local constant created here.
Each type may optionally have presentational info about
the variable (vid) inside. Content Model
Consider
Pattern: Consistency
Pattern: ConsistencyNamespaceDocumentationNo documentation available.Content Model
Consistency
Pattern: Const
Pattern: ConstNamespaceDocumentationNormal local constant introduced e.g. by Let or Consider
presentational info may be given in vid.Content Model
Const
Pattern: ConstrCounts
Pattern: ConstrCountsNamespaceDocumentationConstructor counts are used probably for renumerating.
The article named can be given if not implicit.
This implementation might change in some time.Content Model
ConstrCounts
Pattern: ConstrDef
Pattern: ConstrDefNamespaceDocumentationConstrDef holds a term together with types of its variables and
the top-level functor. Used now mainly for identify.Content Model
ConstrDef
Pattern: Constructor
Pattern: ConstructorNamespaceDocumentationConstructors are functors, predicates, attributes, etc.
nr, kind and aid (article id) determine the constructor
absolutely in MML, relnr optionally gives its serial number
in environment for a particular article (it is not in prels).
All have (possibly empty) properties, argtypes
and some have one or more mother types.
The optional final Fields are selectors for agrregates and structmodes.
aggregbase is for aggregates (maybe OVER-arguments),
structmodeaggrnr is for structmodes (nr of corresponding aggregate).
absredefnr and redefaid optionally give absolute address of
a redefinition. Content Model
Constructor
Pattern: Constructors
Pattern: ConstructorsNamespaceDocumentationConstructors, either imported from other articles ( after accommodation)
- the signature is implicit in that case, or exported from the current
article - then the signature has to be specified.
aid optionally specifies its article's name in uppercase. Content Model
Constructors
Pattern: Correctness
Pattern: CorrectnessNamespaceDocumentationThis is a way how to state all correctness conditions in one keyword.
The relevant conditions are computed by the analyzer and printed
here, their conjunction has to be justified.Content Model
Correctness
Pattern: CorrectnessCondition
Pattern: CorrectnessConditionNamespaceDocumentationThe possible correctness conditions are following.
They can either be only stated in the Correctness,
which conjugates them and proves them all, or come
separately as a proposition with a justification.Content Model
(
%UnknownCorrCond; | %Coherence; | %Compatibility; | %Consistency; | %Existence; | %Uniqueness;
)
Pattern: DefFunc
Pattern: DefFuncNamespaceDocumentationPrivate functor. First come the types of arguments, then
its definition and the result type.
For easier presentation, nr optionally contains number
of the private functor created here, and its identifier's number (vid).Content Model
DefFunc
Pattern: DefMeaning
Pattern: DefMeaningNamespaceDocumentationDefMeaning consists of the formulas and terms defining a constructor.
It can be either defined by _equals_ (terms) or
by _means_ (formulas). It may contain several
partial (case) definitions - first in them comes the
definition (term or formula) valid in that case and second comes
the case formula. The final term or formula specifies the default
case, it is mandatory if no partial definitions are given.
If no default is given, the disjunction of all case formulas must
be true (this have to be proved using the _consistency_ condition).Content Model
DefMeaning
Pattern: DefPred
Pattern: DefPredNamespaceDocumentationPrivate predicate. First come the types of arguments, then
its definition.
For easier presentation, nr optionally contains number
of the private predicate created here, and its identifier's number (vid).Content Model
DefPred
Pattern: DefTheorem
Pattern: DefTheoremNamespaceDocumentationTheorems created from definitions are now printed
as separate top-level items after definitional blocks,
constrkind and constrnr determine the defined constructor.
If they do not appear, this is a canceled (verum) deftheorem. Content Model
DefTheorem
Pattern: Definiens
Pattern: DefiniensNamespaceDocumentationDefiniens of a constructor. This overlaps a bit with Constructor.
defnr is the number of the corresponding definitional theorem, and
vid optionally its label's identifier.
First come the argument types and possibly also the result type.
The optional formula is conjunction of all assumptions if any given.
If this is a redefinition, essentials are indeces of arguments
corresponding to the arguments of original, otherwise it is just
identity. This could be now encode with just one number like the
superfluous does for Constructor.
Optionally the article id (aid) and order in article (nr)
can be given.
relnr optionally gives its serial number
in environment for a particular article (it is not in prels).
vid gives a number of the label identifier if present. Content Model
Definiens
Pattern: Definientia
Pattern: DefinientiaNamespaceDocumentationDefinientia, either imported from other articles ( after accommodation)
- the signature is implicit in that case, or exported from the current
article - then the signature has to be specified.
aid optionally specifies article's name in uppercase.Content Model
Definientia
Pattern: Definition
Pattern: DefinitionNamespaceDocumentationDefinition of a functor, predicate, mode, attribute or structure.
with optional label, properties and correctness conditions.
Sometimes no constructor is created (e.g. for expandable modes).
The second optional form creating three or more constructors
is for structure definitions, which define the aggregate functor,
the structure mode, the strict attribute and zero or more selectors,
and create existential registration for the strict attribute.
If any definientia and definitional theorems are created,
they follow immediately after the enclosing definitional block
(this might be changed in the future).
Number, position, and identifier number of the definiens
(vid) can be optionally given.Content Model
Definition
Pattern: DefinitionBlock
Pattern: DefinitionBlockNamespaceDocumentationA block of one or more (possibly canceled) (re)definitions,
possibly with assumptions. If any definientia and
definitional theorems are created, they follow immediately
after this block. Content Model
DefinitionBlock
Pattern: EndPosition
Pattern: EndPositionNamespaceDocumentationEnding position (e.g. of blocks).Content Model
EndPosition
Pattern: ErrorCluster
Pattern: ErrorClusterNamespaceDocumentationThis encodes error during cluster processingContent Model
ErrorCluster
Pattern: ErrorFrm
Pattern: ErrorFrmNamespaceDocumentationIncorrect (erroneous formula) - e.g. containing undefined symbolsContent Model
ErrorFrm
Pattern: ErrorIdentify
Pattern: ErrorIdentifyNamespaceDocumentationThis encodes error during identification processingContent Model
ErrorIdentify
Pattern: ErrorTrm
Pattern: ErrorTrmNamespaceDocumentationIncorrect (erroneous term) - e.g. containing undefined symbolsContent Model
ErrorTrm
Pattern: Existence
Pattern: ExistenceNamespaceDocumentationNo documentation available.Content Model
Existence
Pattern: FCluster
Pattern: FClusterNamespaceDocumentationFunctor (term) cluster.
This says that Term with ArgTypes has Cluster (optionally followed
by its extended version created by rounding up in current environment),
optionally with explicit Typ.
Optionally the article id (aid) and order in article (nr)
can be given.Content Model
FCluster
Pattern: Fields
Pattern: FieldsNamespaceDocumentationSpecify fields of aggregates and structmodes by their relative
nr.
Optionally the article id (aid) and order in article (absnr)
can be given.
The selector kind (kind) 'U' can can be added explicitly.Content Model
Fields
Pattern: For
Pattern: ForNamespaceDocumentationUniversally quantified formula
If available, presentational info is given in pid.
If available, numbere of the variable identifier is
given in vid. Content Model
For
Pattern: Format
Pattern: FormatNamespaceDocumentationFormat keeps the kind of a given symbol and arities.
For bracket formats (K) this keeps both symbols.
Optionally a nr (of the format) is kept, to which patterns may refer,
This implementation might change in some time.Content Model
Format
Pattern: Formats
Pattern: FormatsNamespaceDocumentationFormat info contains symbol formats and priorities.
Priorities are used only for functor symbols.
This implementation might change in some time.Content Model
Formats
Pattern: FraenkelNamespaceDocumentationFraenkel term is defined by the types of its lambda arguments,
its lambda term and the separating formula.
Each type may optionally have presentational info about
the variable (vid) inside.Content Model
Fraenkel
Pattern: FreeVar
Pattern: FreeVarNamespaceDocumentationFree variable - used only internally in checkerContent Model
FreeVar
Pattern: From
Pattern: FromNamespaceDocumentationFrom encodes one scheme justification, it cannot be linked.Content Model
From
Pattern: FromExplanations
Pattern: FromExplanationsNamespaceDocumentationReports from the Mizar schematizer - scheme instantioations.
They are now only available when the verifier is compiled with a special
directive - this should be changed to a user option eventually. Content Model
FromExplanations
Pattern: Func
Pattern: FuncNamespaceDocumentationFunctor terms - schematic, aggregates, normal and selectors
Optionally the article id (aid) and order in article (absnr)
can be given. If available, presentational info
(number of the Pattern) is given in pid.Content Model
Func
Pattern: GeneralPolynomial
Pattern: GeneralPolynomialNamespaceDocumentationNo documentation available.Content Model
(
%Polynomial; | %Number;
)
Pattern: Given
Pattern: GivenNamespaceDocumentationThis is existential assumption, it may be used when the normal
assumption starts with existential quantifier, and emulates
the use of assume followed by consider.
First comes the reconstructed assumed existential statement, then
the newly introduced local constant(s), and finally the proposition(s)
containing the new local constant(s).
For easier presentation, nr optionally contains the number
of the first local constant created here.
Each type may optionally have presentational info about
the variable (vid) inside. Content Model
Given
Pattern: Identify
Pattern: IdentifyNamespaceDocumentationIdentification (unoriented, this is not used currently, see identifyWithExp instead).
This says that two terms with the two constructors at the top
are equal when the pairs of their arguments specified in EqArgs
are equal.
Optionally the article id (aid) and order in article (nr)
can be given.Content Model
Identify
Pattern: IdentifyRegistration
Pattern: IdentifyRegistrationNamespaceDocumentationOne justified identification registration. The correctness conditions
could be made more specific.Content Model
IdentifyRegistration
Pattern: IdentifyRegistrations
Pattern: IdentifyRegistrationsNamespaceDocumentationIdentifications, either imported from other articles ( after accommodation)
- the signature is implicit in that case, or exported from the current
article - then the signature has to be specified.
aid optionally specifies its article's name in uppercase. Content Model
IdentifyRegistrations
Pattern: IdentifyWithExp
Pattern: IdentifyWithExpNamespaceDocumentationIdentification (oriented, currently used version).
This says to identify anything matching the first term
or formula pattern (with ConstrKind and ConstrNr as the top
constructor) with the second pattern (instantiated by the matching).
The type requirements for the matching (i.e. the loci) are given first.
Note that this works only one way, if you want it also the other way, the
symmetrical variant has to be explicitly stated as another identification.
Optionally the article id (aid) and order in article (nr)
can be given.Content Model
IdentifyWithExp
Pattern: InfConst
Pattern: InfConstNamespaceDocumentationInference constant - used for internal term sharingContent Model
InfConst
Pattern: IntNamespaceDocumentationSingle integerContent Model
Int
Pattern: Is
Pattern: IsNamespaceDocumentationQualification formula (claims that a term has certaing type)Content Model
Is
Pattern: It
Pattern: ItNamespaceDocumentation_It_ is a special term used in definitions.
Probably no longer used on this level.Content Model
It
Pattern: IterEquality
Pattern: IterEqualityNamespaceDocumentationIterative equality. The optional numbers (nr) is serial label
numbering, and original label identifier (vid).Content Model
IterEquality
Pattern: IterStep
Pattern: IterStepNamespaceDocumentationThis is one step in an iterative equation.Content Model
IterStep
Pattern: JustifiedPropertyNamespaceDocumentationA property of a constructor, the proposition expreesing it,
and its justification.Content Model
JustifiedProperty
Pattern: JustifiedTheoremNamespaceDocumentationTheorem as a proposition with justification.Content Model
JustifiedTheorem
Pattern: LambdaVar
Pattern: LambdaVarNamespaceDocumentationLambda variable - unused nowContent Model
LambdaVar
Pattern: Let
Pattern: LetNamespaceDocumentationIntroduction of local constants, the numbering is automatic,
so only types are needed.
For easier presentation, nr optionally contains the number
of the first local constant created here.
Each type may optionally have presentational info about
the variable (vid) inside. Content Model
Let
Pattern: LocusVar
Pattern: LocusVarNamespaceDocumentationLocus variable used usually for pattern matching.
Their types are given elsewhere in data using them - see e.g. ConstructorContent Model
LocusVar
Pattern: Monomial
Pattern: MonomialNamespaceDocumentationMonomial has a coefficient and a series of variables with their exponents. Content Model
Monomial
Pattern: Not
Pattern: NotNamespaceDocumentationNegation.
If available, presentational info is given in pid.Content Model
Not
Pattern: NotationBlock
Pattern: NotationBlockNamespaceDocumentationBlock of synonyms or antonyms. The patterns are
semantically irrelevant and are not printed yet - fix this.Content Model
NotationBlock
Pattern: Notations
Pattern: NotationsNamespaceDocumentationNotations, either imported from other articles ( after accommodation)
- the signature is implicit in that case, or exported from the current
article - then the signature and vocabularies have to be specified.
aid optionally specifies article's name in uppercase. Content Model
Notations
Pattern: Now
Pattern: NowNamespaceDocumentationDiffuse statement - its thesis is reconstructed in the end.
Label (nr) and its identifier (vid) of diffuse statement
(if any) is label of its thesis.Content Model
Now
Pattern: Num
Pattern: NumNamespaceDocumentationNumeralContent Model
Num
Pattern: Number
Pattern: NumberNamespaceDocumentationNo documentation available.Content Model
(
%RationalNr; | %ComplexNr;
)
Pattern: Pair
Pattern: PairNamespaceDocumentationThis is a pair of integersContent Model
Pair
Pattern: Pattern
Pattern: PatternNamespaceDocumentationPatterns map formats with argtypes to constructors.
The format is either specified as a number (then it must
be available in some table), or is given explicitely.
Visible are indeces of visible (nonhidden) arguments.
If antonymic, its constructor has to be negated. Mode patterns
can have expansion instead of just a constructor - this might
be done for other patterns too, or replaced by the _equals_
mechanism. The J (forgetful functor) patterns are actually
an example of another expanded patterns, but the expansion
is uniform for all of them, so it does not have to be given.
The invalid ConstrKind J is now used for forgetful functors,
this should be changed.
Optionally the article id (aid) and order in article (nr)
can be given. relnr optionally gives its serial number
in environment for a particular article (it is not in prels).
redefnr optonally gives the relative number of the
original pattern to which the current is defined as synonym/antonym.Content Model
Pattern
Pattern: PerCases
Pattern: PerCasesNamespaceDocumentationThis justifies the case split (the disjunction of all Suppose
or Case items in direct subblocks) in PerCasesReasoning.
The case split is only known after all subblocks are known,
so this is the last item in its block, not like in the Mizar text.Content Model
PerCases
Pattern: PerCasesReasoning
Pattern: PerCasesReasoningNamespaceDocumentationReasoning per cases. It only contains CaseBlock or
SupposeBlock subblocks, with the exception of the mandatory
last PerCases justifying the case split.
Direct and diffuse versions are possible
(this depends on the kind of its parent block).
The block thesis is printed for proofs in the beginning and
for diffuse reasoning in the end.Content Model
PerCasesReasoning
Pattern: PolyEval
Pattern: PolyEvalNamespaceDocumentationBuiltin numerical evaluations of arithmetical functors
and predicates. For predicates, the value can be false.
Arguments are generally polynoms with complex coefficients.
For functors, the last polynom is the result value.Content Model
PolyEval
Pattern: Polynomial
Pattern: PolynomialNamespaceDocumentationPolynomial consists of several monomials.Content Model
Polynomial
Pattern: PredNamespaceDocumentationAtomic predicate formulas - schematic, attributive and normal
Optionally the article id (aid) and order in article (absnr)
can be given. If available, presentational info
(number of the Pattern) is given in pid.Content Model
Pred
Pattern: PrivFunc
Pattern: PrivFuncNamespaceDocumentationPrivate functor with arguments is a shorthand for another term.
The first (mandatory) term is the expansion, arguments follow.Content Model
PrivFunc
Pattern: PrivPred
Pattern: PrivPredNamespaceDocumentationPrivate predicate with arguments is a shorthand for another formulaContent Model
PrivPred
Pattern: Proof
Pattern: ProofNamespaceDocumentationDirect proof of some proposition (which is the proof's thesis).
Label (nr) of proof (if any) is label of its thesis, vid is then
the identifier nr of this label.Content Model
Proof
Pattern: Properties
Pattern: PropertiesNamespaceDocumentationProperties of constructors; if some given, the first and the
second argument to which they apply must be specified.Content Model
Properties
Pattern: PropositionNamespaceDocumentationProposition is a sentence with position and possible label (and its identifier).Content Model
Proposition
Pattern: QuaTrm
Pattern: QuaTrmNamespaceDocumentationQua terms capture the retyping term qua type construct,
but they are probably no longer used on this level.Content Model
QuaTrm
Pattern: RCluster
Pattern: RClusterNamespaceDocumentationExistential (registration) cluster.
This says that exists Typ with Cluster (optionally followed
by its extended version created by rounding up in current environment).
Optionally the article id (aid) and order in article (nr)
can be given. Content Model
RCluster
Pattern: RationalNr
Pattern: RationalNrNamespaceDocumentationRational numbersContent Model
RationalNr
Pattern: Reasoning
Pattern: ReasoningNamespaceDocumentationReasoning is a series of skeleton and auxiliary items,
finished by optional per cases reasoning.Content Model
(
(
%SkeletonItem; | %AuxiliaryItem;
)
)*
,
%PerCasesReasoning;
?
%EndPosition;
Pattern: Reconsider
Pattern: ReconsiderNamespaceDocumentationFirst comes the series of target types and reconsidered terms.
For all these terms a new local variable with its target type
is created, and its equality to the corresponding term is remembered.
Finally the proposition about the typing is given and justified.
For easier presentation, nr optionally contains the number
of the first local constant created here.
Each type may optionally have presentational info about
the variable (vid) inside. Content Model
Reconsider
Pattern: Ref
Pattern: RefNamespaceDocumentationReference can be either private (coming from the current article)
- their number is the position at the stack of accessible
references (so it is not unique), or library - these additionally
contain their kind (theorem or definition) and article nr.
The position in the inference is kept for error messaging.
For a private inference, the vid attribute optionally tells
its identifier's number.Content Model
Ref
Pattern: Registration
Pattern: RegistrationNamespaceDocumentationOne justified cluster registration. The correctness conditions
could be made more specific for each.Content Model
Registration
Pattern: RegistrationBlock
Pattern: RegistrationBlockNamespaceDocumentationBlock of cluster registrations.
Content Model
RegistrationBlock
Pattern: Registrations
Pattern: RegistrationsNamespaceDocumentationRegistrations, either imported from other articles ( after accommodation)
- the signature is implicit in that case, or exported from the current
article - then the signature has to be specified.
aid optionally specifies its article's name in uppercase. Content Model
Registrations
Pattern: Requirement
Pattern: RequirementNamespaceDocumentationRequirement is a constructor specially treated by the system.
We give its internal number and optionally its name and
the article id (aid) and order in article (absnr).Content Model
Requirement
Pattern: Requirements
Pattern: RequirementsNamespaceDocumentationRequirements (now only the exported form).Content Model
Requirements
Pattern: Reservation
Pattern: ReservationNamespaceDocumentationReservation of a new variable for a type.
The type may optionally have presentational info about
the variable (vid) inside.Content Model
Reservation
Pattern: Scheme
Pattern: SchemeNamespaceDocumentationSchemes keep types of their second-order variables.
First comes the scheme thesis, then the premises.
The article number and order in article can be given,
otherwise it belongs to the current article and order is implicit.
Optional aid attribute specifies article name.Content Model
Scheme
Pattern: SchemeBlock
Pattern: SchemeBlockNamespaceDocumentationScheme blocks are used for declaring the types of second-order
variables appearing in a scheme, and for its justification.
This could be a bit unified with Scheme later.
schemenr is its serial nr in the article, while vid is
its identifier number. Content Model
SchemeBlock
Pattern: SchemeFuncDecl
Pattern: SchemeFuncDeclNamespaceDocumentationDeclaration of a scheme functor, possibly with its identifier number.Content Model
SchemeFuncDecl
Pattern: SchemeInstantiation
Pattern: SchemeInstantiationNamespaceDocumentationInstantions of scheme functors and predicates.
and predicates. Scheme functors can be instantiated
to other functors or terms (if zero arity). Scheme predicates
can be instantiated to other predicates Content Model
SchemeInstantiation
Pattern: SchemePredDecl
Pattern: SchemePredDeclNamespaceDocumentationDeclaration of a scheme predicate, possibly with its identifier number.Content Model
SchemePredDecl
Pattern: Schemes
Pattern: SchemesNamespaceDocumentationSchemes, either imported from other articles ( after accommodation)
- the signature is implicit in that case, or exported from the current
article - then the signature has to be specified.
aid optionally specifies article's name in uppercase.Content Model
Schemes
Pattern: Section
Pattern: SectionNamespaceDocumentationNo documentation available.Content Model
Section
Pattern: Set
Pattern: SetNamespaceDocumentationThis is e.g.: set a = f(b); . The type of the new local constant
is given. This local constant is now always expanded to its
definition, and should not directly appear in any expression,
but it is now needed for some implementation reasons.
For easier presentation, nr optionally contains the number
of the first local constant created here.
The type may optionally have presentational info about
the variable (vid) inside. Content Model
Set
Pattern: Signature
Pattern: SignatureNamespaceDocumentationSignature is a list of articles from which we import constructors.Content Model
Signature
Pattern: SkeletonItem
Pattern: SkeletonItemNamespaceDocumentationSkeleton items change the InFile.Current thesis, for Proof the
changed Thesis together with used expansions is printed
explicitely after them.
PerCasesReasoning is not included here.Content Model
(
%Let; | %Conclusion; | %Assume; | %Given; | %Take; | %TakeAsVar;
)
%Thesis;
?
Pattern: SkippedProof
Pattern: SkippedProofNamespaceDocumentationThis means that the author has skipped the proof.
Articles with such items are not yet fully completed.Content Model
SkippedProof
Pattern: StructLoci
Pattern: StructLociNamespaceDocumentationStructural loci are not used yet (that is all I know about them).Content Model
StructLoci
Pattern: Suppose
Pattern: SupposeNamespaceDocumentationSupposition of one or more propositions.Content Model
Suppose
Pattern: SupposeBlock
Pattern: SupposeBlockNamespaceDocumentationBlock starting with one supposition, the direct and diffuse version
(this depends on the kind of its parent block).
The block thesis is printed for proofs in the beginning and
for diffuse reasoning in the end.Content Model
SupposeBlock
Pattern: Symbols
Pattern: SymbolsNamespaceDocumentationLocal dictionary for an article.
The symbol kinds still use very internal notation. Content Model
Symbols
AttributesAttributeTypeUseDocumentationaid
xsd:stringOptional
Pattern: Take
Pattern: TakeNamespaceDocumentationTake without equality. This does not introduce a new local constant,
just changes the thesis.Content Model
Take
Pattern: TakeAsVar
Pattern: TakeAsVarNamespaceDocumentationTake with equality. This introduces a new local constant,
whose type is given here.
For easier presentation, nr optionally contains the number
of the first local constant created here.
The type may optionally have presentational info about
the variable (vid) inside. Content Model
TakeAsVar
Pattern: TheoremsNamespaceDocumentationTheorems, either imported from other articles ( after accommodation)
- the signature is implicit in that case, or exported from the current
article - then the signature has to be specified.
They can be either ordinary or definitional.
The article number and order in article can be given,
otherwise it belongs to the current article and order is implicit.
Optional aid attribute specifies article name.
constrkind and constrnr determine for def. theorems
the defined constructor. If they do not appear (and kind='D'),
then this is a canceled (verum) deftheorem. Content Model
Theorems
Pattern: Thesis
Pattern: ThesisNamespaceDocumentationThe changed thesis is printed after skeleton items in proofs,
together with the numbers of definientia used for its expansion.Content Model
Thesis
Pattern: ThesisExpansions
Pattern: ThesisExpansionsNamespaceDocumentationNumbers of Definiens used in expanding the thesis,
together with their counts.Content Model
ThesisExpansions
Pattern: Typ
Pattern: TypNamespaceDocumentationParameterized type - either mode or structure
The kinds "L" and "G" are equivalent, "G" is going to be
replaced by more correct "L" in Mizar gradually.
First goes the LowerCluster, than UpperCluster
Optionally the article id (aid) and order in article (absnr)
can be given. If available, presentational info
(number of the Pattern) is given in pid, and
presentational info about variable introduced (e.g. in Fraenkel)
may be given in vid.Content Model
Typ
Pattern: Uniqueness
Pattern: UniquenessNamespaceDocumentationNo documentation available.Content Model
Uniqueness
Pattern: UnknownCorrCond
Pattern: UnknownCorrCondNamespaceDocumentationNo documentation available.Content Model
UnknownCorrCond
Pattern: Var
Pattern: VarNamespaceDocumentationNormal bound variable (deBruijn index).
Their types are given in quantification - see For, Fraenkel Content Model
Var
Pattern: Verum
Pattern: VerumNamespaceDocumentationVerum (true formula)Content Model
Verum
Pattern: Vocabularies
Pattern: VocabulariesNamespaceDocumentationVocabularies keep for each article its symbol numbers.
This implementation might change in some time.Content Model
Vocabularies