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Proof step 6 from proof le-2pot-01 (previous step)

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

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 < i + 1, i0 ≤ 2 ^ i, 0 ≤ j0, j0 < 2, 0 ≤ i, 0 ≤ i0, 0 ≤ 2 ^ i ⊦ i0 * 2 + j0 ≤ 2 ^ (i + 1)-1 * 2 + 1

Rule argument

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

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%lels-04: ⊦ i ≤ j → (¬ ¬ j < i ↔ false); 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 Used terms: i + 1, 2