G.277 numbers prime number

VII.23

If two numbers be prime to one another, the number which measures the one of them is prime to the remaining number.
numbers_prime_number(A, B, C)
given A, B be two numbers prime to one another, let any number C measure A
prove C, B are also prime to one another
A B C D
given A, B be two numbers prime to one another, let any number C measure A
assert If C, B are not prime to one another, some number will measure C, B
assert Let a number measure them, and let it be D
assert D measures C, and C measures A,
assert D also measures A
assert It also measures B
∵ numbers_prime_measured_defassert D measures A, B which are prime to one another ⇒⇐
assert no number will measure the numbers C, B
∴ C, B are prime to one another

Dependency Graph

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Required for

G.278, G.279, G.280, G.281, G.297, G.298, G.303, G.304, G.305, G.306, G.314, G.315, G.316, G.317, G.323, G.325, G.326, G.327, G.328, G.329, G.330, G.331, G.332, G.333, G.334, G.335, G.337, G.338, G.339, G.342, G.343, G.345, G.364, G.370, G.381, G.383, G.403, G.404, G.405, G.406, G.407, G.408, G.409, G.413, G.414, G.415, G.419, G.420, G.423, G.425, G.427, G.429, G.431, G.433, G.437, G.438, G.439, G.440, G.443, G.444, G.445, G.448, G.449, G.450, G.451, G.452, G.458, G.459, G.460, G.464, G.465, G.466, G.467, G.468, G.470, G.472, G.474, G.476, G.477, G.480, G.481, G.482, G.486, G.487, G.488, G.491, G.492, G.493, G.494, G.495, G.496, G.497, G.584, G.589, G.597, G.600, G.601