29 lines
963 B
Text
29 lines
963 B
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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-/
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prelude
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import init.core init.wf
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notation `Σ` binders `, ` r:(scoped p, sigma p) := r
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notation `Σ'` binders `, ` r:(scoped p, psigma p) := r
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universes u v
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lemma ex_of_psig {α : Type u} {p : α → Prop} : (Σ' x, p x) → ∃ x, p x
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| ⟨x, hx⟩ := ⟨x, hx⟩
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section
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variables {α : Type u} {β : α → Type v}
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protected lemma sigma.eq : ∀ {p₁ p₂ : Σ a : α, β a} (h₁ : p₁.1 = p₂.1), (eq.rec_on h₁ p₁.2 : β p₂.1) = p₂.2 → p₁ = p₂
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| ⟨a, b⟩ ⟨.(a), .(b)⟩ rfl rfl := rfl
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end
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section
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variables {α : Sort u} {β : α → Sort v}
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protected lemma psigma.eq : ∀ {p₁ p₂ : psigma β} (h₁ : p₁.1 = p₂.1), (eq.rec_on h₁ p₁.2 : β p₂.1) = p₂.2 → p₁ = p₂
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| ⟨a, b⟩ ⟨.(a), .(b)⟩ rfl rfl := rfl
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end
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