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Proof step 9 from proof leone-two (previous step)

j0 < 2, 3 < i0 * 2 + j0, 0 < i0 * 2 + j0, 1 < i0 * 2 + j0, i0 ≤ 1, 0 ≤ j0, 0 ≤ i0 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult name: modlep-03 seq: j * i + j0 ≤ j * i0 + j1, 0 ≤ j0, j0 < j, abs(j1) < j ⊦ i ≤ i0 subst: [j, i, j0, i0, j1] → [2, 1, 1, i0, j0]

Additional information

Used simplifier rules: ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ 0 < i → (i ≤ 1 ↔ i = 1); (s)% ⊦ i = 1 → i * j = j; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 ≤ i → abs(i) = i; (s)%j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s) Used terms: 2, 1, 1, i0, j0