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Proof step 27 from proof fits-law-shr (previous step)

(b2i(by) + 1) / 2 ^ band(i, 31) < ~127, 0 ≤ band(i, 31), b2i(by) < ~1, b2i(by) < 0, 0 < band(i, 31), band(i, 31) < 32, (b2i(by) + 1) / 2 ^ band(i, 31) < 0, b2i(by) < (b2i(by) + 1) / 2 ^ band(i, 31) ⊦ b2i(by) +1 < ~127, (b2i(by) + 1) / 2 ^ band(i, 31) = b2i(i2b((b2i(by) + 1) / 2 ^ band(i, 31) - 1)) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i < j ∧ j < i0 → i +1 < i0 subst: [i, j, i0] → [b2i(by), (b2i(by) + 1) / 2 ^ band(i, 31), ~127] rotate: F spec: int-basic1 inst: name: lf-01

Additional information

Used simplifier rules: byte-nls: ⊦ ¬ b2i(by) < ~128;% ⊦ band(i, j) = band(j, i);% ⊦ i + j = j + i;% ⊦ i +1 = i + 1;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: b2i(by), (b2i(by) + 1) / 2 ^ band(i, 31), ~127