2014-08-01 17:37:55 +00:00
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logic
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=====
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2014-12-15 21:13:04 +00:00
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Logical constructions and theorems, beyond what has already been
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2015-07-29 20:30:18 +00:00
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declared in init.datatypes and init.logic.
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2014-08-01 17:37:55 +00:00
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2015-07-29 20:30:18 +00:00
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The command `import logic` does not import any axioms by default.
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2014-10-05 17:50:13 +00:00
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2014-12-15 21:13:04 +00:00
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* [connectives](connectives.lean) : the propositional connectives
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2014-12-01 05:19:56 +00:00
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* [eq](eq.lean) : additional theorems for equality and disequality
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2014-10-05 17:50:13 +00:00
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* [cast](cast.lean) : casts and heterogeneous equality
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* [quantifiers](quantifiers.lean) : existential and universal quantifiers
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* [identities](identities.lean) : some useful identities
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2014-12-15 21:13:04 +00:00
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* [instances](instances.lean) : class instances for eq and iff
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* [subsingleton](subsingleton.lean)
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* [default](default.lean)
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2014-10-05 17:50:13 +00:00
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2015-07-29 20:30:18 +00:00
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The file `choice.lean` declares a choice axiom, and uses it to
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prove the excluded middle, propositional completeness, axiom of
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choice, and prove that the decidable class is trivial when the
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choice axiom is assumed.
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* [choice](choice.lean)
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2014-12-15 21:13:04 +00:00
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Subfolders:
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2014-10-05 17:50:13 +00:00
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2014-08-23 01:10:22 +00:00
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* [examples](examples/examples.md)
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