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Proof step 28 from proof no-leading-zero-04 (previous step)

i = i1 * 256 + j ∧ j ≤ 0 ∧ abs(j) < 256 ∧ i1 ≤ 0 ∧ 0 < 256, int2bytes(i) + i2b(j) ' = i2b(~1) ' + by ' + bytes, i1 = i + 1, i2b(j) ∈ bytes, b2i(by) < 0, i < ~256, i < 0, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ j = 0, bytes = [], ¬ i2b(~1) ∈ int2bytes(i) ∧ i2b(~1) ≠ i2b(j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
~1 = 255 * i1 + j, int2bytes(i1 * 256 + j) + i2b(j) ' = i2b(~1) ' + by ' + bytes, j < 0, i1 * 256 + j < 0, i1 ≤ 0, ~256 < j, i1 * 256 + j < ~256, b2i(by) < 0, i2b(j) ∈ bytes, ∀ bytes, by, i0. i→n(i0) < i→n(i1 * 256 + j) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ bytes = [], j = 0, ¬ i2b(~1) ∈ int2bytes(i1 * 256 + j) ∧ i2b(~1) ≠ i2b(j)

Rule argument

Additional information

Used simplifier rules: ⊦ by ∈ by0 ' ↔ by = by0;% ⊦ by ∈ bytes + bytes0 ↔ ¬ ¬(by ∈ bytes ∨ by ∈ bytes0);% ⊦ by ∈ bytes → by ∈ bytes0 + bytes;% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ by ' + bytes = bytes0 → by ∈ bytes0; (forward)% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ bytes + by ' = bytes0 → by ∈ bytes0; (forward)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ i < 0 → abs(i) = ~ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i = (* i1) * i + j0 ↔ 0 = (i1 - 1) * i + j0;% ⊦ i + j = j + i;