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Proof step 10 from proof div-rec (previous step)

j * (i1 + 1) + j0 = i0 * j + j1, j1 < j, j0 < j, 0 < j, 0 ≤ j0, 0 ≤ i1, 0 ≤ j1, 0 < i0 * j + j1 ⊦ i0 = i1 + 1

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modeqp seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [i0, j, j1, i1 + 1, j0] flags: []

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0, j, j1, i1 + 1, j0