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Proof step 27 from proof bytes2int-diff (previous step)

bytes2int(bytes2) * 256 + band(b2i(by), 255) = bytes2int(bytes3) * 256 + band(b2i(by0), 255), # bytes2 = # bytes3, ∀ bytes0, bytes1. # bytes1 < #(bytes3 + by0 ') → # bytes0 = # bytes1 ∧ bytes2int(bytes0) = bytes2int(bytes1) → bytes0 = bytes1 ⊦ by = by0, bytes2 + by ' = bytes3 + by0 ', bytes3 = []

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 28:
i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1
Proof step 29:
bytes2int(bytes2) = bytes2int(bytes3) ∧ band(b2i(by), 255) = band(b2i(by0), 255), bytes2int(bytes2) * 256 + band(b2i(by), 255) = bytes2int(bytes3) * 256 + band(b2i(by0), 255), # bytes2 = # bytes3, ∀ bytes0, bytes1. # bytes1 < #(bytes3 + by0 ') → # bytes0 = # bytes1 ∧ bytes2int(bytes0) = bytes2int(bytes1) → bytes0 = bytes1 ⊦ by = by0, bytes2 + by ' = bytes3 + by0 ', bytes3 = []

Rule argument

seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [bytes2int(bytes2), 256, band(b2i(by), 255), bytes2int(bytes3), band(b2i(by0), 255)] rotate: F spec: int-mult inst: name: modeqp

Additional information

Used simplifier rules: ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ 256 ≤ band(i, 255); Used terms: bytes2int(bytes2), 256, band(b2i(by), 255), bytes2int(bytes3), band(b2i(by0), 255)