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Proof step 56 from proof pot2-est-div6 (previous step)

(i0 + 1) * 6 < 2 ^ i0, j0 < 6, 2 ^ i0 ≤ (j0 + 1) + i0 * 6, 36 ≤ i0 * 6 + j0, 0 ≤ j0, 0 ≤ i0, 0 < i0 * 6 + j0, (i0 + 1) * 6 ≤ i0 * 6 + j0 ⊦ (j0 + 1) + i0 * 6 ≤ 6 + i0 * 6

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: le-add seq: ⊦ i + j ≤ i0 + j ↔ i ≤ i0 subst: [i0, j, i] → [6, i0 * 6, j0 + 1] flags: rewrite

Additional information

Used simplifier rules: numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; 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 Used terms: 6, i0 * 6, j0 + 1