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Proof step 38 from proof no-leading-zero-01 (previous step)

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 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 39:
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 ⊦

Rule argument

fma: i - 256 < 256 * i + j

Additional information

Used simplifier rules: ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ i * j + i = i * (j + 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used formulas: i - 256 < 256 * i + j