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Proof step 44 from proof no-leading-zero-01 (previous step)

i < 256 * i + 256 * 1, 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 + 256 * 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 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ j < (* i1) * j + i ↔ 0 < (i1 - 1) * j + i subst: [i, i1, j] → [256 * 1, 256, i] rotate: F spec: int-mult inst: name: numls-12

Additional information

Used simplifier rules: int2bytes-byte: ~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) ';% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;% ⊦ 0 < i ∧ j < 0 → ((* j) < (* i) * i0 ↔ (j + 1 - i) / i < i0);% ⊦ i < 0 → (~2 < i ↔ i = ~1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j + i = i * (j + 1);% ⊦ by ' = by0 ' + bytes ↔ by = by0 ∧ bytes = [];%~128 ≤ i, i ≤ 127, ~128 ≤ j, j ≤ 127, i ≠ j ⊦ i2b((* i)) ≠ i2b((* j));% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: 256 * 1, 256, i