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Why doesn't simplify() simplify symbolic equations?

Consider the following sage code:

a,b,c = var('a b c')

simplify(a + b == a + c)

I would expect the result of this code to be b == c, but sage gives me a + b == a + c. The only way to actually simplify the equation is to use add_to_both_sides(-a). For more complicated equations this seems to be hardly applicable. Why doesn't simplify() (or full_simplify()) take care of this properly?