The phrase "proof of equivalence" is correct and usable in written English.
This phrase is typically used to refer to mathematical proofs in which two mathematical statements have been shown to be equal. For example, "After completing the proof of equivalence, the mathematician was able to establish that the two equations were indeed equal."
The proof of equivalence was accomplished using the formulas simplified in this paper.
The proof of equivalence relies heavily on the character theory of finite Abelian groups.
Given what are classically two variants of a single set-theoretic principle, their classical proof of equivalence requires at some point an instance of the excluded middle.
The paper shows how to construct the circuit and provides a proof of equivalence between the circuit and the LP QPproblemlem.
To complete our proof of equivalence of all inequalities in this theorem and in Lemma 2.1, it suffices to show further the following implications.
However, in general this proof of equivalence will not carry through to an intuitionistic context, and thus what are classically two forms of one principle may result into two distinct principles when working intuitionistically.
The mathematics of these notions and the associated proofs of equivalence are intricate and a presentation of them is beyond the scope of this entry.
The logic of Equalities with Uninterpreted Functions is used in the formal verification community mainly for proofs of equivalence: proving that two versions of a hardware design are the same, or that input and output of a compiler are semantically equivalent are two prominent examples of such proofs.
So the absence of a significant difference is not a proof for equivalence of the GMO and the counterpart, or "absence of evidence is not evidence of absence" [ 18, 19].
It contains the germ of a mathematical equivalence proof, but it does not contain a rigorous proof of equivalency: the mathematical framework that Schrödinger associated with wave mechanics is a space of continuous and normalizable functions, which is too small to establish the appropriate relation with matrix mechanics.
For a proof of the equivalence of the three characterizations see, e.g., (Du and Ko 2000).
