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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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Enrico Tassi