59 lines
1.6 KiB
Text
59 lines
1.6 KiB
Text
/-
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Copyright (c) 2016 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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Authors: Leonardo de Moura
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-/
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prelude
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import init.data.repr
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universes u v
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inductive ordering
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| lt | eq | gt
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instance : has_repr ordering :=
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⟨(λ s, match s with | ordering.lt := "lt" | ordering.eq := "eq" | ordering.gt := "gt")⟩
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namespace ordering
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def swap : ordering → ordering
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| lt := gt
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| eq := eq
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| gt := lt
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@[inline] def or_else : ordering → ordering → ordering
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| lt _ := lt
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| eq o := o
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| gt _ := gt
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theorem swap_swap : ∀ (o : ordering), o.swap.swap = o
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| lt := rfl
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| eq := rfl
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| gt := rfl
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end ordering
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def cmp_using {α : Type u} (lt : α → α → Prop) [decidable_rel lt] (a b : α) : ordering :=
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if lt a b then ordering.lt
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else if lt b a then ordering.gt
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else ordering.eq
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def cmp {α : Type u} [has_lt α] [decidable_rel ((<) : α → α → Prop)] (a b : α) : ordering :=
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cmp_using (<) a b
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instance : decidable_eq ordering :=
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λ a b,
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match a with
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| ordering.lt :=
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(match b with
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| ordering.lt := is_true rfl
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| ordering.eq := is_false (λ h, ordering.no_confusion h)
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| ordering.gt := is_false (λ h, ordering.no_confusion h))
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| ordering.eq :=
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(match b with
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| ordering.lt := is_false (λ h, ordering.no_confusion h)
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| ordering.eq := is_true rfl
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| ordering.gt := is_false (λ h, ordering.no_confusion h))
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| ordering.gt :=
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match b with
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| ordering.lt := is_false (λ h, ordering.no_confusion h)
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| ordering.eq := is_false (λ h, ordering.no_confusion h)
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| ordering.gt := is_true rfl
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