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The ancient Chinese game of Cuju has been recognised by some as the first existence of the game of football being played.
Here is our first existence result.
Our first existence result uses Theorem 2.1.
The first existence result is based on Banach's contraction principle.
Now, we can establish our first existence result.
Our first existence result is based on Lemma 3.1.
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He sees this nebulous state as a third existence melding history, fantasy and personal revelation.
This work was extended into a trilogy including Etzel Andergast (1931) and Joseph Kerkhovens dritte Existenz (1934; Kerkhoven's Third Existence).
Now there are 3 apples (second existence sentence).}.
There are 5 black rabbits (second existence sentence).
Now, our third existence result is based on Leray-Schauder's nonlinear alternative.
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