What does depth refer to in Isar Virtual Machine output?

Question

Here is a proof:

theory Example

imports Main

begin

datatype natural = Zero | Succ natural

lemma "⋀ n. n = Succ m ⟹ n ≠ Zero"
proof -
 fix n
 assume "n = Succ m" 
 from this show "n ≠ Zero" by (metis natural.distinct(2))
qed

end

The depth value is 0 throughout the proof but after

show "n ≠ Zero"

it changes to

proof (prove): depth 1

What does depth mean here? Is it any important when carrying out a proof?

Answer 1

In a nutshell, it refers to the current proof nesting level. In your case, it's 1, because show opens a new proof inside the proof.

To answer your second question: No, it's not important at all. Some people use it to measure how complicated a proof is, but to the system, it makes no difference.