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feat(library/logic/connectives/basic): add not_not_em theorem

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura 2014-08-26 17:30:59 -07:00
parent 0099a7b224
commit 9bea23111f
1 changed files with 5 additions and 0 deletions
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library/logic/connectives/basic.lean
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@ -141,6 +141,11 @@ or_elim H1
(assume H2 : c, or_inl H2) (assume H2 : c, or_inl H2)
(assume H2 : a, or_inr (H H2)) (assume H2 : a, or_inr (H H2))
theorem not_not_em {p : Prop} : ¬¬(p ∨ ¬p) :=
assume not_em : ¬(p ∨ ¬p),
have Hnp : ¬p, from
assume Hp : p, absurd (or_inl Hp) not_em,
absurd (or_inr Hnp) not_em
-- iff -- iff
-- --- -- ---