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Proof step 53 from proof bytes2int-int2bytes-len-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ abs(i) < j → i % j = i

Rule argument

seq: ⊦ abs(i) < j → i % j = i subst: [j, i] → [256, band(b2i(by), 255)] rotate: F spec: int-div inst: name: mod-zero-05

Additional information

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