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Let's say that I'm trying to prove the following:

Theorem le_s_n : forall n m, S n <= S m -> n <= m.

I feel like it might be productive to perform induction on the pair (n, m). The cases would be something like (0, 0), (0, S m'), (S n', 0), and (S n', S m'). Is this at all possible?

Carl Patenaude Poulin
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    You could try to do that but it won't be very productive. A more promising approach is to examine the (inductive) evidence `S n <= S m`. – ejgallego May 15 '17 at 04:20

1 Answers1

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You could have a look at this answer to have a glimpse on lexicographic ordering, but I suggest to read @ejgallego comments, that I totally agree with.

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