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Proof step 19 from proof bytes2int-rec-first-zero (previous step)

bytes2int(i2b(0) ' + by ' + bytes1) = band(b2i(by), 255) * 256 ^ n→i(# bytes1) + bytes2int(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) ⊦ bytes1 = [], 256 * (band(b2i(by), 255) * 256 ^ n→i(# bytes1) + bytes2int(i2b(0) ' + bytes1)) = bytes2int(i2b(0) ' + bytes1) * 256 + 256 ^ (n→i(# bytes1) + 1) * band(b2i(by), 255)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [n→i(# bytes1), 256] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ 0 ≤ n→i(n);% ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i * j + i * j0 = i * (j + j0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); Used terms: n→i(# bytes1), 256