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Proof step 46 from proof pot2-est-div6 (previous step)

6 * (i1 + 4) < 8 * (i1 + 4), 8 * 2 ^ i1 ≤ 6 * (i1 + 4), 1 + 6 * (3 + i1) + j0 ≤ 6 * (i1 + 4), 0 ≤ i1, 0 < (3 + i1) * 6 + j0, 8 * 2 ^ i1 ≤ (3 + i1) * 6 + j0 + 1, 36 ≤ (3 + i1) * 6 + j0, 0 ≤ j0, 4 * 2 ^ i1 ≤ 3 * (4 + i1), j0 < 6 ⊦ 8 * 2 ^ i1 < 8 * (i1 + 4)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: forward-lels seq: ⊦ i ≤ j ∧ j < j0 → i < j0 subst: [j, j0, i] → [6 * (i1 + 4), 8 * (i1 + 4), 8 * 2 ^ i1] flags: rewrite

Additional information

Used simplifier rules: numls: ⊦ (* i1) * j < (* i2) * j ↔ 0 < (i2 - i1) * j; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%numlsledel-01: i0 ≠ 0, i0 < i ⊦ (* i) ≤ j → (* i0) < j; 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%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%le-dist-01: ⊦ i * (j + i0) + j1 ≤ i * (j0 + i0) ↔ i * j + j1 ≤ i * j0; from specification int-mult%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs%numlsledel: j0 ≠ 0, j < j0 ⊦ i ≤ (* j) → i < (* j0); from specification int-abs%ls-pos: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: 6 * (i1 + 4), 8 * (i1 + 4), 8 * 2 ^ i1