44 lines
1.1 KiB
Markdown
44 lines
1.1 KiB
Markdown
init
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====
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The files in this folder are required by low-level operations, and
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are always imported by default. You can suppress this behavior by
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beginning a file with the keyword "prelude".
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Syntax declarations:
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* [reserved_notation](reserved_notation.lean)
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* [tactic](tactic.lean)
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* [priority](priority.lean)
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Datatypes and logic:
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* [datatypes](datatypes.lean)
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* [logic](logic.lean)
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* [bool](bool.lean)
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* [num](num.lean)
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* [nat](nat.lean)
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Support for well-founded recursion:
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* [relation](relation.lean)
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* [wf](wf.lean)
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* [wf_k](wf_k.lean)
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* [measurable](measurable.lean)
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Additional datatypes:
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* [prod](prod.lean)
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* [sigma](sigma.lean)
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The default import:
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* [default](default.lean)
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Module init.logic defines "inhabited" and "nonempty"
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types. Constructively, inhabited types have a witness, while nonempty
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types 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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