Use the "existsi" tactic to provide a specific element a : A for which PP a holds.

Use the "cases" tactic to decompose the existential quantifier.

Use the "have" tactic to introduce a contradiction.

Use the "apply" tactic with an assumption of type ∃ x : A, PP x.

It demonstrates the distributive property of conjunction over disjunction.

It demonstrates the commutative property of conjunction.

It demonstrates the equivalence between proving R from P or Q, and proving R from P and then Q.

It demonstrates the equivalence between proving R from P and Q, and proving R from P under the assumption Q.

exact p,

apply q2r,

exact r,

The middle is excluded

The third is not given

Reduction to the absurd

Evidence must be built

Classical logic is used only for computer science, while Intuitionistic logic is used for pure mathematics.

Intuitionistic logic rejects the use of variables like P and Q.

Classical logic assumes every statement is either true or false, while Intuitionistic logic equates truth with provability.

Intuitionistic logic allows for statements to be 'partially true', whereas Classical logic does not.

They are logically equivalent and EM can be used to derive RAA.

Lean's standard library includes RAA as a primitive tactic, but EM must be imported.

EM is used for constructive proofs, while RAA is used for non-constructive proofs.

RAA is a part of intuitionistic logic, while EM is only found in classical logic.

Because Lean's constructor tactic cannot be applied to a goal containing a disjunction.

Because the negation of a conjunction is logically weaker than the negation of a disjunction in all logical systems

Because the truth table for De Morgan's Laws shows a contradiction in the second law when P and Q are both false.

Because it requires the principle that every proposition is either true or false to select a specific side of the disjunction.