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Proof step 9 from proof bytes2int-rec-first-zero (previous step)

∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → bytes0 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes0) = band(b2i(by), 255) * 256 ^ n→i(# bytes0) + bytes2int(i2b(0) ' + bytes0) ⊦ band(255, b2i(by0)) + 256 * bytes2int((i2b(0) ' + by ') + bytes1) = bytes2int(i2b(0) ' + bytes1 + by0 ') + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)
Proof step 11:
i2b(0) ' + bytes1 ≠ [], ∀ by, bytes0. # bytes0 < #(bytes1 + by0 ') → true → bytes0 = [] ∨ bytes2int(i2b(0) ' + by ' + bytes0) = band(b2i(by), 255) * 256 ^ n→i(# bytes0) + bytes2int(i2b(0) ' + bytes0) ⊦ band(255, b2i(by0)) + 256 * bytes2int((i2b(0) ' + by ') + bytes1) = (bytes2int(i2b(0) ' + bytes1) * 256 + band(b2i(by0), 255)) + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)

Rule argument

name: bytes2int-rec rotate: F subst: [by, bytes] → [by0, i2b(0) ' + bytes1]

Additional information

Used simplifier rules: ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ by ' ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: by0, i2b(0) ' + bytes1