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

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: 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] flags: []

Additional information

Used simplifier rules: leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%num-between: i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%numlelsdel: j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: 2, 1, 1, i0, j0