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Proof step 27 from proof no-leading-zero (previous step)

int2bytes(bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', 0 ≤ b2i(by), bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255) < 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ 0 ≤ j1 ∧ j1 < j → (i0 * j + j1 < j ↔ i0 ≤ 0)
Proof step 29:
0 ≤ band(b2i(by0), 255) ∧ band(b2i(by0), 255) < 256, int2bytes(bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', 0 ≤ b2i(by), bytes2int(i2b(0) ' + by ' + bytes1) ≤ 0, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

Rule argument

seq: ⊦ 0 ≤ j1 ∧ j1 < j → (i0 * j + j1 < j ↔ i0 ≤ 0) subst: [j1, j, i0] → [band(b2i(by0), 255), 256, bytes2int(i2b(0) ' + by ' + bytes1)] rotate: F spec: int-mult inst: name: ls-add

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ 256 ≤ band(i, 255); Used terms: band(b2i(by0), 255), 256, bytes2int(i2b(0) ' + by ' + bytes1)