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Proof step 23 from proof no-leading-zero-04 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
int2bytes(i / 256 - 1) + i2b(i % 256) ' = i2b(~1) ' + by ' + bytes, i / 256 < ~256, i / 256 ≤ i, i < 0, i < ~256, b2i(by) < 0, i2b(i % 256) ∈ bytes, i ≤ ~256, i / 256 ≤ ~256, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ bytes = [], i % 256 = 0, ¬ i2b(~1) ∈ int2bytes(i / 256 - 1) ∧ i2b(~1) ≠ i2b(i % 256)

Rule argument

Additional information

Used simplifier rules: j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0);% ⊦ 0 < j → (i / j ≤ 0 ↔ i < j);% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;%0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0;% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i ≤ i0 ∧ j0 ≥ 0 → i ≤ i0 + j0;% ⊦ ¬ i < j ↔ j ≤ i;