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Proof step 2 from proof pot2-pos-03 (previous step)

2 ^ j ≤ 2 * i, i < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i < 0 ∧ 0 < j → ¬ j ≤ i

Rule argument

spec: int-abs inst: name: zero-gels-02 seq: ⊦ i < 0 ∧ 0 < j → ¬ j ≤ i subst: [i, j] → [2 * i, 2 ^ j] flags: rewrite

Additional information

Used simplifier rules: pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;%two-minus: ⊦ i < 0 → 2 ^ i = 0;%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: 2 * i, 2 ^ j