2014-08-01 17:37:55 +00:00
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logic
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=====
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2014-12-01 05:19:56 +00:00
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Additional constructions and axioms. By default, `import logic` does not
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import any axioms.
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2014-08-01 17:37:55 +00:00
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2014-10-05 17:50:13 +00:00
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Logical operations and 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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Constructively, inhabited types have a witness, while nonempty types
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are "proof irrelevant". Classically (assuming the axioms in
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logic.axioms.hilbert) the two are equivalent. Type class inferences
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are set up to use "inhabited" however, so users should use that to
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declare that types have an element. Use "nonempty" in the hypothesis
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of a theorem when the theorem does not depend on the witness chosen.
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2014-08-01 17:37:55 +00:00
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* [axioms](axioms/axioms.md) : additional axioms
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2014-08-23 01:10:22 +00:00
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* [examples](examples/examples.md)
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