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Proof step 46 from proof no-leading-zero (previous step)

b2i(by) = 0, int2bytes(band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', by0 ∈ int2bytes(band(b2i(by0), 255)), i2b(0) ∈ int2bytes(band(b2i(by0), 255)), 0 ≤ band(b2i(by0), 255), band(b2i(by0), 255) < 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦ true ∈ bytes2bits(bytes1), true ∈ byte2bits(i2b(0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 47:
⊦ 0 ≤ b2i(by) → band(b2i(by), 255) = b2i(by)
Proof step 48:
¬ 0 ≤ b2i(by0), b2i(by) = 0, int2bytes(band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', by0 ∈ int2bytes(band(b2i(by0), 255)), i2b(0) ∈ int2bytes(band(b2i(by0), 255)), 0 ≤ band(b2i(by0), 255), band(b2i(by0), 255) < 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦ true ∈ bytes2bits(bytes1), true ∈ byte2bits(i2b(0))
Proof step 55:
0 ≤ b2i(by0), b2i(by) = 0, int2bytes(b2i(by0)) = i2b(0) ' + by ' + bytes1 + by0 ', by0 ∈ int2bytes(b2i(by0)), i2b(0) ∈ int2bytes(b2i(by0)), 0 ≤ b2i(by0), b2i(by0) < 256, ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦ true ∈ bytes2bits(bytes1), true ∈ byte2bits(i2b(0))

Rule argument

seq: ⊦ 0 ≤ b2i(by) → band(b2i(by), 255) = b2i(by) subst: [by] → [by0] rotate: F spec: byte inst: name: byte-011x-pos

Additional information

Used terms: by0