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Proof step 92 from proof bytes2int-int2bytes-len-eq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 93:
b2i(by) = 0, # bytes1 = # int2bytes(bytes2int(bytes1)), bytes2int(bytes1) < 0, bytes2int(bytes1) < ~1, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes1 = [], bytes1 + by ' = int2bytes(bytes2int(bytes1)) + i2b(0) ', bytes2int(bytes1) * 256 = ~256

Rule argument

Additional information

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