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Proof step 2 from proof count-i2j-length (previous step)

i ≤ j ⊦ # count-i2j(i, j) = i→n(j - i) + 1

User applied rule induction

And obtained the following new goals

Proof step 3:
i ≤ j, ∀ j0, i0. i→n(j0 - i0) < i→n(j - i) → i0 ≤ j0 → # count-i2j(i0, j0) = i→n(j0 - i0) + 1 ⊦ # count-i2j(i, j) = i→n(j - i) + 1

Rule argument

indvar: i→n(j - i) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(j - i)