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Proof step 31 from proof pot2-est-div6 (previous step)

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), 2 ^ i1 < i1 + 4, 8 * 2 ^ i1 ≤ 6 * (i1 + 4), j0 ≤ 5 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 33:
0 < i1, 0 ≤ i1, 0 < (3 + i1) * 6 + j0, 8 * 2 ^ i1 -1 * 2 ≤ (3 + i1) * 6 + j0 + 1, 36 ≤ (3 + i1) * 6 + j0, 0 ≤ j0, 4 * 2 ^ i1 -1 * 2 ≤ 3 * (4 + i1), 2 ^ i1 -1 * 2 < i1 + 4, 8 * 2 ^ i1 -1 * 2 ≤ 6 * (i1 + 4), j0 ≤ 5 ⊦

Rule argument

spec: inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i1, 2] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = 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%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs%numleledel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; from specification int-abs%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%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs Used terms: i1, 2