ZeroToLean/Index.md

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)
basicLogic.p_or_p_equal_p	or_self	(a \lor a) = a
basicLogic.p_or_p_iff_p		a \lor a \iff a
basicLogic.and_or_distributivity_left	and_or_left	a \land (b \lor c) \iff (a \land b) \lor (a \land c)
basicLogic.and_or_distributivity_right	and_or_right	(a \land b) \lor c \iff (a \lor c) \land (b \lor c)
basicLogic.p_and_true_equal_p	and_true	(a \land True) = a
basicLogic.p_and_true_iff_p		a \land True \iff a
basicLogic.true_and_p_equal_p	true_and	(True \land a) = a
basicLogic.true_and_p_iff_p		True \land a \iff a
basicLogic.p_or_false_equal_p	or_false	(a \lor False) = a
basicLogic.p_or_false_iff_p		a \lor False \iff a
basicLogic.false_or_p_equal_p	false_or	(False \lor a) = a
basicLogic.false_or_p_iff_p		False \lor a \iff a
basicLogic.and_false_equal_false	and_false	(a \land False) = False
basicLogic.and_false_iff_false		a \land False \iff False
basicLogic.false_and_equal_false	false_and	(False \land a) = False
basicLogic.false_and_iff_false		False \land a \iff False
basicLogic.or_true_equal_true	or_true	(a \lor True) = True
basicLogic.or_true_iff_true		a \lor True \iff True
basicLogic.true_or_equal_true	true_or	(True \lor a) = True
basicLogic.true_or_iff_true		True \lor a \iff True