# [isabelle] Dealing with lets in Isar

Dear All,
We have a question about how to deal conveniently with
Lets in Isar proofs. Some of our definitions contain many
nested lets, as in
definition
"foo f e1 e2 e3 == let (x, y) = e1; (u, v) = e2; (w, k) = e3 in f x y u v w k"
The problem is that we have foo unfolded in our premises, say
lemma
assumes "P (let (x, y) = e1; (u, v) = e2; (w, k) = e3 in f x y u v w k)"
shows "thesis"
We could prove such lemmas with
lemma
assumes "P (let (x, y) = e1; (u, v) = e2; (w, k) = e3 in f x y u v w k)"
shows "thesis"
proof -
from assms
obtain x y u v w k
where "P (f x y u v w k)" and
"(x, y) = e1" and "(u, v) = e2" and "(w, k) = e3" by ...
but we are wondering whether there is a simpler way. Essentially,
we want to avoid having to fix the variables and to avoid to write
the equations explicitly. We rather prefer the way how the cases-construction
works, which automatically fixes variables and puts such equations
into the context, for example
lemma
assumes "P (n:: nat)"
shows "thesis"
proof (cases n)
In this example you have "n = 0" in the "first" case and fix nat/n = Suc nat
in the "second" case. Is there something similar for many nested lets?
If not, how would we have to go about implementing (presumably in ML)
such a construction?
Best wishes,
Christian

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