Following on from the previous posts in the series, now it's time to prove that subtracting from both sides of an equation and that multiplying both sides of an equation preserve equality -- more proofs in the algebra series. Also below I'll discuss the difficulty of proving that dividing both sides of an equation preserves equality and start on some helper proofs in that regard.
First, as before, a section in which I copy in any theorems from the previous posts that are used in this post's derivations:
[in progress]
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