2014-09-16 18:44:50 +00:00
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logic.core
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==========
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2014-08-01 17:37:55 +00:00
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Logical operations and connectives.
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* [prop](prop.lean) : the type Prop
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* [eq](eq.lean) : equality and disequality
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2014-08-28 01:39:55 +00:00
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* [connectives](connectives.lean) : propositional connectives
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2014-08-01 17:37:55 +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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* [if](if.lean) : if-then-else
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2014-08-22 20:23:45 +00:00
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* [identities](identities.lean) : some useful identities
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2014-09-16 18:44:50 +00:00
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* [examples](examples/examples.md)
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Type classes for general logical manipulations:
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* [inhabited](inhabited.lean) : inhabited types
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* [nonempty](nonempty.lean) : nonempty type
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* [decidable](decidable.lean) : decidable types
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* [instances](instances.lean) : type class instances
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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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