G.355 even number even

IX.24

If from an even number an even number be subtracted, the remainder is even.
even_number_even()
prove / A C / is even
A C B
construct From the even number / A B / let the even number / B C / be subtracted :
∵ even_number_divisible_defassert / A B / is even, it has a half part
assert For the same reason / B C / also has a half part
∴ So that the remainder [/ A C / also has a half part, and] / A C / is therefore even

Dependency Graph

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Required for

G.356, G.357, G.358