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Proof step 42 from proof no-leading-zero-01 (previous step)

i < 256 * (i + 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 + 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

Proof step 43:
⊦ i * (j + j0) = i * j + i * j0
Proof step 44:
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 ⊦

Rule argument

seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [1, i, 256] rotate: F spec: int-mult inst: name: dist-rsplit

Additional information

Used terms: 1, i, 256