More specifically, if we have an equational theory $T$ (a set of equations understood as being implicitly universally quantified), are the (equational) consequences of $T$ that can be proved with substitution and the properties of equality the same as the universally quantified equations which can be proved from $T$ with these rules in addition to the normal rules of first-order logic?
2026-03-29 23:30:28.1774827028
Is the full strength of first-order logic needed for dealing with equational theories?
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