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Proof step 30 from proof no-leading-zero-04 (previous step)

0 = 255 * i1 + j + 1, ~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)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ j < 0 ∧ ¬ i0 < i → i0 ≠ i + j subst: [j, i, i0] → [j + 1, 255 * i1, 0] rotate: F spec: int-basic2 inst: name: neq

Additional information

Used simplifier rules: int2bytes-byte: ~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) ';% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < 0 → (~1 ≤ i ↔ i = ~1);% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;%i < 0 ⊦ (* i) + j = j - ~ i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ 0 < i → (i * j = 0 ↔ j = 0);% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ 0 < i ∧ j < 0 → ((* i) * i0 < (* j) ↔ i0 < j / i);% ⊦ i < 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 < (* j) ↔ i0 < (i + j - 1) / i);% ⊦ i < 1 ↔ i ≤ 0;% ⊦ bytes + by ' = bytes0 → by ∈ bytes0; (forward)% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ by ' + bytes = bytes0 → by ∈ bytes0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ bytes + bytes0 = bytes + bytes1 ↔ bytes0 = bytes1;% ⊦ by ' = by0 ' + bytes ↔ by = by0 ∧ bytes = []; Used terms: j + 1, 255 * i1, 0