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20 lines
1.2 KiB
Markdown
20 lines
1.2 KiB
Markdown
### Basic logic
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| Name | Mathlib equivalent | Proposition |
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|---------------|--------------------|-------------|
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|`basicLogic.and_commutative` | `and_comm` | $$a\land b \iff b \land a$$ |
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|`basicLogic.or_commutative` | `or_comm` | $$a\lor b \iff b \lor a$$ |
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|`basicLogic.double_negation` | `not_not_intro`| $$a\to\neg\neg a$$ |
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|`basicLogic.and_associative` | `and_assoc`| $$a\land (b\land c) \iff (a\land b) \land c$$|
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|`basicLogic.contrapositive` | `contrapose` | $$(a \to b) \to (\neg b \to \neg a)$$|
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|`basicLogic.p_or_p_equal_p` | `or_self` | $$(a \or a) = a$$|
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|`basicLogic.p_or_p_iff_p` | | $$a \or a \iff a$$|
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|`basicLogic.and_or_distributivity_left` | `and_or_left` | $$a \and (b \or c) \iff a \and b \or a \and c$$|
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|`basicLogic.and_or_distributivity_right` | `and_or_right` | $$a \and b \or c \iff (a \or c) \and (b \or c)$$ |
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|`basicLogic.p_and_true_equal_p` | `and_true` | $$(a \and True) = a$$|
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|`basicLogic.p_and_true_iff_p` | | $$a \and True \iff a$$|
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|`basicLogic.true_and_p_equal_p` | `true_and` | $$(True \and a) = a$$|
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|`basicLogic.true_and_p_iff_p` | | $$True \and a \iff a$$|
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|`basicLogic.p_or_false_equal_p` | `or_false` | $$(a \or False) = a$$|
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|`basicLogic.p_or_false_iff_p` | | $$a \or False \iff a$$|
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