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new math
(a·b)·c = a·(b·c)
a·b = b·a
e·a = a
a·e = a
z·a = z
a·z = z
a·a = a
(a·b)·(c·d) = (a·c)·(b·d)
a·(b·c) = (a·b)·(a·c)
(b·c)·a = (b·a)·(c·a)
a·b = a·c → b = c
b·a = c·a → b = c