first little proofs

Index.md

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+### Basic logic
+
+| Name | Mathlib equivalent | Proposition |
+|---------------|--------------------|-------------|
+|`basicLogic.and_commutative` | `and_comm` | $$a\land b \iff b \land a$$ |
+|`basicLogic.or_commutative` | `or_comm` | $$a\lor b \iff b \lor a$$ |
+|`basicLogic.double_negation` | `not_not_intro`| $$a\to\neg\neg a$$ |
+|`basicLogic.and_associative` | `and_assoc`| $$a\land (b\land c) \iff (a\land b) \land c$$|
+|`basicLogic.contrapositive` | `contrapose` | $$(a \to b) \to (\neg b \to \neg a)$$|