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Proof step 9 from proof mod-succ-01 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult 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] → [i1, j, j1, i0, 1 + j0]

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; (s)%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)% ⊦ i < j + 1 ↔ i ≤ j; (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: i1, j, j1, i0, 1 + j0