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Proof step 10 from proof ls-mult-2pot (previous step)

j * 2 ^ i < 2 ^ (i1 + i) ∧ 2 ^ (i1 + i) ≤ 2 ^ i → j * 2 ^ i < 2 ^ i, 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ls-pos-2pot: ⊦ 0 ≤ j → (2 ^ j < 2 ^ j0 ↔ j < j0);%two-le: ⊦ 0 ≤ i → (2 ^ i ≤ 2 ^ j ↔ i ≤ j);%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%zero-gels-03: ⊦ i < 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lep-01: ⊦ i + j ≤ i ↔ j ≤ 0; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs