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Proof step 52 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 ⊦ 0 ≤ 256 + b2i(by0) ∧ 256 + b2i(by0) ≤ 127, true ∈ bytes2bits(bytes1), true ∈ byte2bits(i2b(0))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;