[isabelle] Proving nth on a sorted list monotone
I am stumblingly trying to prove that nth is monotone on a sorted
list, I got this far:
"sorted (xs::int list)"
shows "xs ≠  ⟶ mono (λ a . xs ! a)"
proof (induct xs rule: sorted.induct)
case 1 show ?case by simp
case (2 element) show ?case
proof (simp add: mono_def)
And here I am stuck, do I have to explicitly assume that the indices
are within the length of xs, or how does a proof with a partial
All the best
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