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Proof step 6 from proof pot2-est-div6 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 8:
0 < i0 * 6 + j0, j0 < 6, 0 < i0, 2 ^ i0 -1 * 2 ≤ (i0 + 1) * 6, 2 ^ i0 -1 * 2 ≤ (i0 * 6 + j0) + 1, 36 ≤ i0 * 6 + j0, 0 ≤ j0, 0 ≤ 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)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 1 ≤ i ↔ 0 < i; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs Used terms: i0, 2