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1 | include "basics/jmeq.ma". |
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2 | include "basics/types.ma". |
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3 | include "basics/list.ma". |
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4 | |
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5 | definition inject : ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ λA,P,a,p. dp … a p. |
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6 | definition eject : ∀A.∀P: A → Prop.(Σx:A.P x) → A ≝ λA,P,c.match c with [ dp w p ⇒ w]. |
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7 | |
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8 | coercion inject nocomposites: ∀A.∀P:A → Prop.∀a.∀p:P a.Σx:A.P x ≝ inject on a:? to Σx:?.?. |
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9 | coercion eject nocomposites: ∀A.∀P:A → Prop.∀c:Σx:A.P x.A ≝ eject on _c:Σx:?.? to ?. |
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10 | |
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11 | (*axiom VOID: Type[0]. |
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12 | axiom assert_false: VOID. |
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13 | definition bigbang: ∀A:Type[0].False → VOID → A. |
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14 | #A #abs cases abs |
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15 | qed. |
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16 | |
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17 | coercion bigbang nocomposites: ∀A:Type[0].False → ∀v:VOID.A ≝ bigbang on _v:VOID to ?.*) |
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18 | |
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19 | lemma sig2: ∀A.∀P:A → Prop. ∀p:Σx:A.P x. P (eject … p). |
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20 | #A #P #p cases p #w #q @q |
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21 | qed. |
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22 | |
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23 | (* END RUSSELL **) |
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