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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
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 ⊦

Rule argument

Additional information

Used simplifier rules: two-minus: ⊦ i < 0 → 2 ^ i = 0;%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i < i + j ↔ 0 < j; (s)% ⊦ i +1 = i + 1; (s)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1% ⊦ i < j → ¬ j < i; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)