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Proof step 12 from proof leone-two (previous step)

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

Additional information

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