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Proof step 7 from proof ls-mult-2pot (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 8:
i1 < j, i1 < 0, j * 2 ^ i < 2 ^ (i1 + i), 0 ≤ i1 + i, 0 ≤ i, 0 < j, i1 + 1 < j ⊦ 2 ^ i < 2 ^ (i1 + i)

Rule argument

fma: 2 ^ i < 2 ^ (i1 + i)

Additional information

Used simplifier rules: ls-pos-2pot: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0);%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: 2 ^ i < 2 ^ (i1 + i)