Let probability of getting the same solution even when the template are not equivalent be (T 1 , T 2 , γ) < 1.
the probability that solution is same for R rounds for t 1 , t 2 which are not equivalent is ≤ R , which can be made arbitrarily small by choosing large R. with a large enough R, obtaining Γ = ∅ from tEMPLEQUIV implies there is a γ under which templates generate equations with the same solution, and by definition, are equivalent.