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Proof step 21 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), ∀ 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 22:
255 < i ⊦ int2bytes(i) = int2bytes(i / 256) + int2bytes(i % 256).last '
Proof step 23:
¬ 255 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), int2bytes(bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) = i2b(0) ' + by ' + bytes1 + by0 ', 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦
Proof step 58:
255 < bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255), int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) / 256) + int2bytes((bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)) % 256).last ' = i2b(0) ' + by ' + bytes1 + by0 ', 0 ≤ b2i(by), ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → int2bytes(bytes2int(i2b(0) ' + by ' + bytes0)) = i2b(0) ' + by ' + bytes0 ∧ 0 ≤ b2i(by) → false ⊦

Rule argument

name: int2bytes-rec-pos rotate: F subst: [i] → [ bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)]

Additional information

Used terms: bytes2int(i2b(0) ' + by ' + bytes1) * 256 + band(b2i(by0), 255)