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Proof step 1 from proof count-one (conclusion)

⊦ count-i2j(j, j) = j '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i ≤ j → count-i2j(i, j) = count-i2j(i, j - 1) + j

Rule argument

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

Additional information

Used simplifier rules: count-empty: ⊦ count-i2j(j, j - 1) = [];%Last: ⊦ ints + i = ints + i '; from specification list[intlista]%Nil: ⊦ [] + ints = ints; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%c-04: ⊦ i ' = i0 ' ↔ i = i0; from specification list[intlista]%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%irreflexivity: ⊦ ¬ i < i; from specification oelem[intlista] Used terms: j, j