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Proof step 4 from proof ls-add (previous step)

i0 * j + j1 < j, j1 < j, 0 ≤ j1, 0 < j, 0 < i0 ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlsp-02 seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [j, i0, j1, 1] flags: current, []

Additional information

Used simplifier rules: one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%one-01: ⊦ i = 1 → i * j = j;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%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 Used terms: j, i0, j1, 1