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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
46 lines
1.8 KiB
Text
46 lines
1.8 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: Leonardo de Moura, Jeremy Avigad, Floris van Doorn
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Sigma types, aka dependent sum.
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-/
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import logic.cast
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open inhabited sigma.ops
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namespace sigma
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universe variables u v
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variables {A A' : Type.{u}} {B : A → Type.{v}} {B' : A' → Type.{v}}
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definition unpack {C : (Σa, B a) → Type} {u : Σa, B a} : C (sigma.mk u.1 u.2) → C u :=
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sigma.rec_on u (λ u1 u2 H, H)
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theorem dpair_heq {a : A} {a' : A'} {b : B a} {b' : B' a'}
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(HB : B == B') (Ha : a == a') (Hb : b == b') : (sigma.mk a b) == (sigma.mk a' b') :=
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hcongr_arg4 @mk (type_eq_of_heq Ha) HB Ha Hb
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protected theorem heq {p : Σa : A, B a} {p' : Σa' : A', B' a'} (HB : B == B') :
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∀(H₁ : p.1 == p'.1) (H₂ : p.2 == p'.2), p == p' :=
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destruct p (take a₁ b₁, destruct p' (take a₂ b₂ H₁ H₂, dpair_heq HB H₁ H₂))
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attribute [instance]
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protected definition is_inhabited [H₁ : inhabited A] [H₂ : inhabited (B (default A))] :
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inhabited (sigma B) :=
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inhabited.destruct H₁ (λa, inhabited.destruct H₂ (λb, inhabited.mk (sigma.mk (default A) b)))
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variables {C : Πa, B a → Type} {D : Πa b, C a b → Type}
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definition dtrip (a : A) (b : B a) (c : C a b) := (sigma.mk a (sigma.mk b c))
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definition dquad (a : A) (b : B a) (c : C a b) (d : D a b c) := (sigma.mk a (sigma.mk b (sigma.mk c d)))
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attribute [reducible]
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definition pr1' (x : Σ a, B a) := x.1
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attribute [reducible]
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definition pr2' (x : Σ a b, C a b) := x.2.1
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attribute [reducible]
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definition pr3 (x : Σ a b, C a b) := x.2.2
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attribute [reducible]
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definition pr3' (x : Σ a b c, D a b c) := x.2.2.1
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attribute [reducible]
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definition pr4 (x : Σ a b c, D a b c) := x.2.2.2
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end sigma
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