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Proof step 2 from proof pot2-pos-04 (previous step)

2 ^ j + 1 < 2 * i, i < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: zero-gels seq: ⊦ i < 0 ∧ 0 ≤ j → ¬ j < i subst: [i, j] → [2 * i, 2 ^ j + 1] flags: rewrite

Additional information

Used simplifier rules: two-lsz: ⊦ ¬ 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%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1 Used terms: 2 * i, 2 ^ j + 1