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Proof step 15 from proof bytes2int-rec-first-zero (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ bytes ≠ [] → bytes2int(bytes + by ') = bytes2int(bytes) * 256 + band(b2i(by), 255)

Rule argument

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

Additional information

Used simplifier rules: bytes2int-zero: ⊦ bytes2int(i2b(0) ') = 0;% ⊦ band(i, j) = band(j, i);% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ by ' ≠ []; Used terms: by, i2b(0) '