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Proof step 87 from proof bytes2int-int2bytes-len-eq (previous step)

(bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256 = 0, # bytes1 = # int2bytes(1 + bytes2int(bytes1)), 0 ≤ band(b2i(by), 255), bytes2int(bytes1) < 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, band(b2i(by), 255) < 256, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 + by ' = int2bytes(1 + bytes2int(bytes1)) + i2b(0) ', bytes1 = [], bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, b2i(by) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i % j = 0 ∧ i + i0 < 0 ∧ i < 0 ∧ 0 ≤ i0 ∧ i0 % j ≠ 0 ∧ 0 < j → (i + i0) % j = i0 % j - j subst: [j, i0, i] → [256, band(b2i(by), 255), bytes2int(bytes1) * 256] rotate: F spec: int-div inst: name: mod-add1-negpos-neg

Additional information

Used simplifier rules: ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;%0 < j ⊦ 0 ≤ i ∧ i < j → i % (* j) = i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + j = j + i;%0 ≤ i, i < 128 ⊦ band(b2i(by), 255) = (* i) ↔ b2i(by) = i;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ i < 0 ∧ j0 < j ∧ 0 ≤ j → i * j + j0 < 0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i * j + i = i * (j + 1);% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;%j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0); Used terms: 256, band(b2i(by), 255), bytes2int(bytes1) * 256