## FIND THINGS: THEOREMS: THEOREMS OF THE FORM "P IMPLIES Q": THEOREMS MENTIONING FINITENESS IN THE HYPOTHESIS

If M is a

**finite**set and H is a proper subset of M, then the cardinality of H is less than the cardinality of M.

**Konig's Lemma**: Every tree having the

**finite-forking property**contains at least one infinite branch.

**Wedderburn's Theorem**: Every

**finite**division ring is a field.

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