G.354 many odd numbers

IX.23

If as many odd numbers as we please be added together, and their multitude be odd, the whole is odd.
many_odd_numbers_ix_23()
prove / A D / is also odd
A B C E D
construct Let as many odd numbers as we please, / A B /, / B C /, / C D /, the multitude of which is odd, be added together
construct Let the unit / D E / be subtracted from / C D /
∵ odd_number_divisible_defassert / C E / is even
∵ many_odd_numbersassert / A C / is also even
∵ many_even_numbersassert / A E / is also even
assert / D E / is an unit
∵ odd_number_divisible_def∴ / A D / is odd

Dependency Graph

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Required for

G.360, G.361, G.362