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Proof step 6 from proof ls-mult-2pot (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
i1 < j, i1 < 0, j * 2 ^ i < 2 ^ (i1 + i), 0 ≤ i1 + i, 0 ≤ i, 0 < j, i1 + 1 < j ⊦

Rule argument

Additional information

Used simplifier rules: two-minus: ⊦ i < 0 → 2 ^ i = 0;%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs