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Proof step 40 from proof no-leading-zero-01 (previous step)

i - 256 < ~383, i - 256 < 256 * i + j, int2bytes(i) = i2b(0) ' + by ' + bytes0, i2b(0) ∈ int2bytes(i), i * 256 + j < 0, i ≤ 0, j ≤ 0, i < 256 * (i + 1) + j, 0 ≤ b2i(by), i * 256 + j < ~383, abs(j) < 256, ∀ bytes, by, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
int2bytes(i) = i2b(0) ' + by ' + bytes0, i2b(0) ∈ int2bytes(i), i * 256 + j < 0, j ≤ 0, 0 ≤ b2i(by), i * 256 + j < ~383, abs(j) < 256, i < ~127, i < 256 * (i + 1) + j, i < 0, ∀ bytes, by, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j + i = i * (j + 1);% ⊦ i - j < i0 ↔ i < j + i0;