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Proof step 12 from proof fits-law-div-stronger (previous step)

~ abs(b2i(by1)) ≤ b2i(by1) / i, b2i(by1) / i < ~128, b2i(by1) / i ≤ abs(b2i(by1)), 0 ≤ abs(b2i(by1)) + b2i(by1) / i, b2i(by1) / i < 0 ⊦ ~ abs(b2i(by1)) < ~128, i = ~1, i = 0, b2i(by1) / i = b2i(i2b(b2i(by1) / i))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i ≤ j ∧ j < j0 → i < j0 subst: [i, j, j0] → [~ abs(b2i(by1)), b2i(by1) / i, ~128] rotate: F spec: int-abs inst: name: forward-lels

Additional information

Used simplifier rules: byte-ngr-01: ⊦ ¬ 128 < abs(b2i(by));% ⊦ ~ i ≤ j ↔ 0 ≤ i + j;% ⊦ i + j = j + i;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ ~ i < j ↔ 0 < j + i;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: ~ abs(b2i(by1)), b2i(by1) / i, ~128