In many paper proofs you see authors substitute variables in equations. For example, if there is an inequality "f(x-y) >= g(x-y)*z, the author simply writes let h=(x-y), therefore "f(h) >= g(h)*z" and continues with the proof.
To do the same in Isabelle, would I have to assume that h=(x-y), is there some other way of doing it? I looked at the "let" feature however that does something completely different.
Specifically, I have:
lemma
fixes f g :: "real⇒real"
assumes "∀x∈S. ∀y∈S. f y - f x ≥ (y-x)*(g x)"
shows "∀x∈S. ∀h. f (x+h) - g x ≥ h*(g x)"
so I am letting h=y-x.
I can show this lemma if I assume that "∀h. ∀x∈S. ∀y∈S. h = y-x". Is this the correct approach?