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Proof step 37 from proof pot2-est-div6 (previous step)

2 ^ i0 * 2 < 5 + i0, 0 < (4 + i0) * 6 + j0, 4 * 2 ^ i0 * 2 ≤ 3 * (5 + i0), 8 * 2 ^ i0 * 2 ≤ (4 + i0) * 6 + j0 + 1, 36 ≤ (4 + i0) * 6 + j0, 0 ≤ j0, 8 * 2 ^ i0 * 2 ≤ 6 * (5 + i0), j0 ≤ 5, 0 ≤ (4 + i0) * 6 + j0, 0 ≤ i0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 39:
0 < (4 + i0) * 6 + j0, (2 ^ i0 -1 * 2) * 2 < 5 + i0, 0 < i0, 0 ≤ i0, 0 ≤ (4 + i0) * 6 + j0, j0 ≤ 5, 8 * (2 ^ i0 -1 * 2) * 2 ≤ 6 * (5 + i0), 0 ≤ j0, 36 ≤ (4 + i0) * 6 + j0, 8 * (2 ^ i0 -1 * 2) * 2 ≤ (4 + i0) * 6 + j0 + 1, 4 * (2 ^ i0 -1 * 2) * 2 ≤ 3 * (5 + i0) ⊦

Rule argument

spec: <toplevel> name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i0, 2] flags: <all paths>

Additional information

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