G.358 odd number even

IX.27

If from an odd number an even number be subtracted, the remainder is odd.
odd_number_even()
prove / A C / is odd
A D C B
construct From the odd number / A B / let the even number / B C / be subtracted
construct Let the unit / A D / be subtracted
∵ odd_number_divisible_defassert / B D / is even
assert / B C / is also even
∵ even_number_evenassert / C D / is even
∵ odd_number_divisible_def∴ / A C / is odd

Dependency Graph

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