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Proof step 31 from proof bytes2int-len-one-01 (previous step)

0 ≤ band(b2i(by), 255), bytes2int(bytes0) * 256 + band(b2i(by), 255) < 128, 0 ≤ bytes2int(bytes0) * 256 + band(b2i(by), 255) ⊦ bytes2int(bytes0) * 256 < 128, bytes0.first = i2b(0), bytes0 = []

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

seq: i + j0 ≤ j, 0 ≤ j0 ⊦ i ≤ j subst: [i, j0, j] → [bytes2int(bytes0) * 256, band(b2i(by), 255), 127] rotate: F spec: int-abs inst: name: ple-02

Additional information

Used simplifier rules: i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j;% ⊦ i + j = j + i;% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 ≤ (* j) ↔ i0 ≤ j / i);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ band(i, j) = band(j, i);% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i);% ⊦ i < 1 ↔ i ≤ 0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: bytes2int(bytes0) * 256, band(b2i(by), 255), 127