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Proof step 9 from proof ls-mult-2pot (previous step)

i1 + 1 < i, j * 2 ^ i < 2 ^ (i1 + i), i1 < 0, 0 < j, i1 + 1 < j, i1 < i, 0 < i, 0 ≤ i, 0 ≤ i1 + i ⊦ 2 ^ i < 2 ^ (i1 + i)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 10:
⊦ i < j ∧ j ≤ j0 → i < j0
Proof step 11:
0 < i, i1 < i, i1 + 1 < j, 0 < j, i1 < 0, j * 2 ^ i < 2 ^ (i1 + i), i1 + 1 < i, 0 ≤ i1 + i, 0 ≤ i, j * 2 ^ i < 2 ^ (i1 + i) ∧ 2 ^ (i1 + i) ≤ 2 ^ i → j * 2 ^ i < 2 ^ i ⊦ 2 ^ i < 2 ^ (i1 + i)

Rule argument

spec: int-abs name: forward-lsle seq: ⊦ i < j ∧ j ≤ j0 → i < j0 subst: [i, j, j0] → [j * 2 ^ i, 2 ^ (i1 + i), 2 ^ i]

Additional information

Used terms: j * 2 ^ i, 2 ^ (i1 + i), 2 ^ i