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Proof step 15 from proof intshiftrsign-abs-le (previous step)

band(j, 31) < 32, i < 0, 0 < band(j, 31), 2 ^ band(j, 31) ≤ i + 1, 0 < (i + 1 - 2 ^ band(j, 31)) / 2 ^ band(j, 31) + i ⊦ band(j, 31) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < 0 ∧ 0 < j → ¬ j ≤ i subst: [i, j] → [i + 1, 2 ^ band(j, 31)] rotate: F spec: int-abs inst: name: zero-gels-02

Additional information

Used simplifier rules: band-notneg: ⊦ 0 ≤ i → ¬ band(i, j) < 0;%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 - i = ~ i;% ⊦ 0 < j → (i ^ j = 0 ↔ i = 0);%j ≠ 0 ⊦ ~ i / j = ~(i / j);%i ≠ 0 ⊦ i / i = 1; Used terms: i + 1, 2 ^ band(j, 31)