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Last change
on this file since 2113 was
1134,
checked in by campbell, 9 years ago
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Extra results for non-failing map updates.
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File size:
870 bytes
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| 1 | include "basics/types.ma". |
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| 2 | |
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| 3 | definition option_map : ∀A,B:Type[0]. (A → B) → option A → option B ≝ |
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| 4 | λA,B,f,o. match o with [ None ⇒ None B | Some a ⇒ Some B (f a) ]. |
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| 5 | |
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| 6 | lemma option_map_none : ∀A,B,f,x. |
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| 7 | option_map A B f x = None B → x = None A. |
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| 8 | #A #B #f * [ // | #a #E whd in E:(??%?); destruct ] |
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| 9 | qed. |
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| 10 | |
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| 11 | lemma option_map_some : ∀A,B,f,x,v. |
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| 12 | option_map A B f x = Some B v → ∃y. x = Some ? y ∧ f y = v. |
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| 13 | #A #B #f * |
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| 14 | [ #v normalize #E destruct |
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| 15 | | #y #v normalize #E %{y} destruct % // |
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| 16 | ] qed. |
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| 17 | |
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| 18 | lemma refute_none_by_refl : ∀A,B:Type[0]. ∀P:A → B. ∀Q:B → Type[0]. ∀x:option A. ∀H:x = None ? → False. |
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| 19 | (∀v. x = Some ? v → Q (P v)) → |
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| 20 | Q (match x return λy.x = y → ? with [ Some v ⇒ λ_. P v | None ⇒ λE. match H E in False with [ ] ] (refl ? x)). |
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| 21 | #A #B #P #Q * |
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| 22 | [ #H cases (H (refl ??)) |
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| 23 | | #a #H #p normalize @p @refl |
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| 24 | ] qed. |
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| 25 | |
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