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Proof step 2 from proof pot2-ls-pred-01 (previous step)

⊦ 2 ^ (i - 1) + 1 < 2 ^ i ↔ 1 < i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 4:
¬ 0 < i ⊦ 2 ^ (i - 1) + 1 < 2 ^ i ↔ 1 < i

Rule argument

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

Additional information

Used simplifier rules: pot2-pos-01: ⊦ 1 < 2 ^ i ↔ 0 < i;%sub-pred: ⊦ i -1 = i - 1; from specification int-abs%numls-08: ⊦ i + j < (* i1) * i ↔ j < (i1 - 1) * i; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < 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%numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs Used terms: i, 2