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Proof step 29 from proof long-shiftzero-in (previous step)

l2i(lo) >> band(j, 63) ≤ abs(l2i(lo)), 0 ≤ l2i(lo), 0 < l2i(lo) >> band(j, 63), 9223372036854775807 < l2i(lo) >> band(j, 63) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
0 < l2i(lo), 9223372036854775807 < l2i(lo) >> band(j, 63), l2i(lo) >> band(j, 63) ≤ l2i(lo), 0 ≤ l2i(lo), 0 < l2i(lo) >> band(j, 63), 9223372036854775807 < l2i(lo) ⊦

Rule argument

Additional information

Used simplifier rules: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward)% ⊦ band(i, j) = band(j, i);% ⊦ 0 ≤ i → abs(i) = i;