fd2c42a8bf
sed -Ei 's/^(\s*)((private |protected )?(noncomputable )?(abbreviation|definition|meta_definition|theorem|lemma|proposition|corollary)\s+\S+\s*)((\s*\[(\S+(\s+[0-9]+)*|priority.*)\])+)\s*/\1attribute \6\n\1\2/' library/**/*.lean tests/**/*.lean sed -Ei 's/\s+$//' library/**/*.lean # remove trailing whitespace
39 lines
1.3 KiB
Text
39 lines
1.3 KiB
Text
/-
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Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Jeremy Avigad, Floris van Doorn
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-/
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import logic.cast
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namespace empty
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protected definition elim (A : Type) : empty → A :=
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empty.rec (λe, A)
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attribute [instance]
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protected definition subsingleton : subsingleton empty :=
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subsingleton.intro (λ a b, empty.elim _ a)
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end empty
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attribute [instance]
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protected definition empty.has_decidable_eq : decidable_eq empty :=
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take (a b : empty), decidable.tt (empty.elim _ a)
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definition tneg.tneg (A : Type) := A → empty
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prefix `~` := tneg.tneg
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namespace tneg
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variables {A B : Type}
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protected definition intro (H : A → empty) : ~A := H
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protected definition elim (H1 : ~A) (H2 : A) : empty := H1 H2
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protected definition empty : ~empty := λH : empty, H
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definition tabsurd (H1 : A) (H2 : ~A) : B := empty.elim _ (H2 H1)
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definition tneg_tneg_intro (H : A) : ~~A := λH2 : ~A, tneg.elim H2 H
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definition tmt (H1 : A → B) (H2 : ~B) : ~A := λHA : A, tabsurd (H1 HA) H2
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definition tneg_pi_left {B : A → Type} (H : ~Πa, B a) : ~~A :=
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λHnA : ~A, tneg.elim H (λHA : A, tabsurd HA HnA)
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definition tneg_function_right (H : ~(A → B)) : ~B :=
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λHB : B, tneg.elim H (λHA : A, HB)
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end tneg
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