Rule of Distribution/Disjunction Distributes over Conjunction/Left Distributive

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Theorem

The disjunction operator is left distributive over the conjunction operator:

Formulation 1

$p \lor \paren {q \land r} \dashv \vdash \paren {p \lor q} \land \paren {p \lor r}$

Formulation 2

$\vdash \paren {p \lor \paren {q \land r} } \iff \paren {\paren {p \lor q} \land \paren {p \lor r} }$