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Proof step 18 from proof fits-law-shr-01 (previous step)

abs(s2i(sho) i>> band(i, 31)) ≤ abs(s2i(sho)) ⊦ 0 < s2i(sho), s2i(sho) i>> band(i, 31) = s2i(i2s(s2i(sho) i>> band(i, 31))), ¬ 0 < s2i(sho) i>> band(i, 31) ∧ ¬ 0 < s2i(sho)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i + j < j ↔ i < 0;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 0 < abs(i) ↔ i ≠ 0;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ 0 < j → abs(j) = j;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;