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We place `Proof_using` in the proper place [`vernac`] and we remove
gross parsing hacks.
The new placement should allow to use the printers and more convenient
structure, and reduce strange coupling between parsing and internal
representation.
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Also add an output test for Suggest Proof Using.
This changes the .aux output: instead of getting a key
>context_used "$hyps;$suggest"
where $hyps is a list of the used hypotheses and $suggest is the
;-separated suggestions (or the empty string if Suggest Proof Using is
unset), there is a key
>context_used "$hyps"
and if Suggest Proof Using is set also a key
>suggest_proof_using "$suggest"
For instance instead of
112 116 context_used "B A;A B;All"
we get
112 116 context_used "B A"
112 116 suggest_proof_using "A B;All"
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- "Proof using p*" means: use p and any section var about p.
- Simplify the grammar/parser for proof using <expression>.
- Section variables with a body (let-in) are pulled in automatically
since they are safe to be used (add no extra quantification)
- automatic clear of "unused" section variables made optional:
Set Proof Using Clear Unused.
since clearing section hypotheses does not "always work" (e.g. hint
databases are not really cleaned)
- term_typing: trigger a "suggest proof using" message also for Let
theorems.
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Proof using can be followed by:
- All : all variables
- Type : all variables occurring in the type
- expr:
- (a b .. c) : set
- expr + expr : set union
- expr - expr : set difference
- -expr : set complement (All - expr)
Exceptions:
- a singleton set can be written without parentheses. This also allows
the implementation of named sets sharing the same name space of
section hyps ans write
- bla - x : where bla is defined as (a b .. x y) elsewhere.
- if expr is just a set, then parentheses can be omitted
This module also implements some AI to tell the user how he could
decorate "Proof" with a "using BLA" clause.
Finally, one can Set Default Proof Using "str" to any string that is
used whenever the "using ..." part is missing. The coding of this
sucks a little since it is the parser that applies the default.
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