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Proof step 11 from proof ls-mult-2pot (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
j * 2 ^ i < 2 ^ i, 0 < i, i1 < i, i1 + 1 < j, 0 < j, i1 < 0, j * 2 ^ i < 2 ^ (i1 + i), i1 + 1 < i, i1 ≤ i, i1 ≤ 0, 0 ≤ i1 + i, 0 ≤ i ⊦

Rule argument

Additional information

Used simplifier rules: ls-pos: ⊦ 1 < i ∧ 0 ≤ j → (i ^ j < i ^ j0 ↔ j < j0);%two-le: ⊦ 0 ≤ i → (2 ^ i ≤ 2 ^ j ↔ i ≤ j);% ⊦ i ≤ i + j ↔ 0 ≤ j; (s)%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + j ≤ i ↔ j ≤ 0; (s)% ⊦ i < j ↔ ¬ j ≤ i; (ss)