### Theorem

A theorem usually admits two deletions. Hypothesis and conclusion. It sometime admits a third deletion if the theorem has a classical name. For example you may want to remember that the theorem stating «In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. » is called «the Pythagorean theorem».
Beware, no hypothesis in a deletion should introduce an object. «If, ... , then the center of P is not trivial» is hard to understand, whereus «Let P be a group. If ..., then the center of P is non trivial» is more clear.
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ted «Aff(X)». What you really want is to recall that «the set of vectors of the form Sum of x_ir_i, with x_i\in X and r_i in the field, where the sum of the r_i is 1» is «the affine hull of X». <span>Theorem A theorem usually admits two deletions. Hypothesis and conclusion. It sometime admits a third deletion if the theorem has a classical name. For example you may want to remember that the theorem stating «In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. » is called «the Pythagorean theorem». Beware, no hypothesis in a deletion should introduce an object. «If, ... , then the center of P is not trivial» is hard to understand, whereus «Let P be a group. If ..., then the center of P is non trivial» is more clear. Hypothesis A first important thing is to always write all hypothesis. Sometime, some hypothesis are given in the beginning of a chapter and are assumed to be true in the whole chapter.