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Proof step 17 from proof bytes2int-mklist-mones-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)
Proof step 19:
mklist(i2b(~1), n) + bytes1 ≠ [], b2i(bytes1.first) < 0, ∀ n, bytes0. # bytes0 < #(bytes1 + by ') → b2i(bytes0.first) < 0 → bytes2int(mklist(i2b(~1), n) + bytes0) = bytes2int(bytes0) ∨ bytes0 = [] ⊦ bytes2int(mklist(i2b(~1), n) + bytes1) * 256 + band(b2i(by), 255) = bytes2int(bytes1) * 256 + band(b2i(by), 255), bytes1 = []

Rule argument

name: bytes2int-rec rotate: F subst: [by, bytes] → [by, mklist(i2b(~1), n) + bytes1]

Additional information

Used simplifier rules: ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ mklist(by, m) = [] ↔ m = 0;% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: by, mklist(i2b(~1), n) + bytes1