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Proof step 29 from proof no-leading-zero-04 (previous step)

~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 cut formula

And obtained the following new goals

Proof step 30:
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)

Rule argument

fma: 0 = 255 * i1 + j + 1

Additional information

Used simplifier rules: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used formulas: 0 = 255 * i1 + j + 1