Mathematics: Analytic or Synthetic?

A central debate in Mathematical Logic is whether Mathematical propositions are 'Analytic', or 'Synthetic'. In an 'Analytic' proposition, the predicate is included in the subject, e. g. 'My sister is female' is Analytic, because 'female' is included in the definition of 'sister'. In a 'Synthetic' proposition, the predicate is not included in the subject, e. g. 'My sister is brunette'. Traditionally, Mathematical propositions have been considered Analytic, because, e. g. in '7+5=12', '12' is included in the definitions of '7', '5', and '+' when conjoined, but Kant has notably argued that they are not, so that such propositions are Synthetic. Contemporary Math Logic has gone to elaborate lengths to demonstrate how all Mathematical operations are derived from the definitions of their elements alone. But a Kantian can easily argue, in response, that any 'Successor Function' is Synthetic, so to whatever extent the latter is essential to such systems, and they do all seem to rely on it to generate the Numbers, these Logics only demonstrate that Mathematics is indeed Synthetic. In Formaterialism, Becoming-Multiple, and Becoming-Integrated are distinct processes, and '+' and '=' are examples of each, respectively. Hence, in any A+B=C, =C is not included in A+B, so 'A+B=C' is Synthetic, e. g. before adding 5 oranges to 7 apples can equal anything, a further process of integration, e. g. homogenizing the two groups as both 'fruit', is required. Since simple Arithmetic is the basis of Mathematics, Mathematical propostions are all Synthetic.