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Proof step 53 from proof no-leading-zero (previous step)

b2i(by) = 0, int2bytes(256 + b2i(by0)) = i2b(0) ' + by ' + bytes1 + by0 ', ~256 ≤ b2i(by0), b2i(by0) < 0, i2b(0) ∈ int2bytes(256 + b2i(by0)), by0 ∈ int2bytes(256 + b2i(by0)), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦ 256 + b2i(by0) ≤ 127, true ∈ bytes2bits(bytes1), true ∈ byte2bits(i2b(0))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: int2bytes-le255 rotate: F subst: [i] → [256 + b2i(by0)]

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i ≤ ~1 ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;%i < ~128 ⊦ ¬ b2i(by) ≤ (* i);% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ (* i) + i0 - (* j) = (i - j) + i0;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i2b(b2i(by)) = by;% ⊦ bytes + bytes0 = bytes + bytes1 ↔ bytes0 = bytes1;% ⊦ by ' = by0 ' + bytes ↔ by = by0 ∧ bytes = [];% ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ by ' ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: 256 + b2i(by0)