Theorem

A $\text{theorem}$ is a statement that can be shown to be true.

A theorem consists of assumptions ( premises ) and a conclusion
Assumptions and the conclusion are statement such that the following is true:

The $\text{proof}$ of a theorem has to establish that the statement of the theorem is true.
The proof can use

• The assumptions of the theorem
• Definitions, known facts and known theorems
• Statements, that are proved within the proof or have already been proved elsewhere
• Logical rules of inference

Minor Terminology

• Theorems are statements that are considered very important

• Less import theorems are sometimes called propositions

  • A less important theorem that is helpful in the proof of other results is often called a $\text{lemma}$

• A $\text{corollary}$ is a theorem that follows immediately from a theorem or a proposition that has been proved

• A $\text{conjecture}$ is a statement that is being proposed to be true statement, usually on the basis of some partial evidence, but a proof is still missing