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Proof step 5 from proof count-rec (previous step)

0 ≤ i1, ∀ j0, i0. i→n(j0 - i0) < i→n(i1) → i0 ≤ j0 → count-i2j(i0, j0) = i0 ' + count-i2j(i0 + 1, j0) ⊦ count-i2j(i, i1 + i) = i ' + count-i2j(i + 1, i1 + i)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: counti2j-rec seq: ⊦ i ≤ j → count-i2j(i, j) = count-i2j(i, j - 1) + j subst: [j, i] → [i1 + i, i] flags: rewrite, current

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i1 + i, i