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G.270 numbers multiplying make¶

If two numbers by multiplying one another make certain numbers, the numbers so produced are equal.

numbers_multiplying_make(A, B, C, D)
given A, B be two numbers, let A by multiplying B make C, B by multiplying A make D
prove C = D

given A, B be two numbers, let A by multiplying B make C, B by multiplying A make D

assert A by multiplying B has made C,

assert B measures C according to the units in A

assert The unit E also measures the number A according to the units in it

assert the unit E measures A the same number of times that B measures C

∵ unit_measure_numberassert alternately, the unit E measures the number B the same number of times that A measures C

assert B by multiplying A has made D,

assert A measures D according to the units in B

assert The unit E also measures B according to the units in it

assert the unit E measures the number B the same number of times that A measures D

assert The unit E measured the number B the same number of times that A measures C

assert A measures each of the numbers C, D the same number of times

∴ C = D

Dependency Graph¶