A: axiom.

$C$ : conjecture.

L: lemma.

$P$ : proposition.

Remark You will lose $0\mathrm{.}5$ pt for each wrong$/$incomplete answer, until you lose all $3$ points

for this question.

are all mathematical statements. Among them,

is a true statement, which does not require any proof.

are also true statements, but require proofs. To clarify the relations

between them: A

is generally $($depending on the author's view$)$ a spe$-$

cial $.$ It encapsulates some technical details, and provides prerequisites

to prove further results $-$ for example fundamental theorems.

might be true or false, yet it has not been proved$/$disproved yet $-$

however, once proved to be true, it becomes a

You feel excited, as you realised this proposition is the last piece you need to prove the

conjecture. Now it is your show time, to return the favour of Jr$.$ Proofini, by proving that

the conjecture is true. First, you have to prove some lemmas.