[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 167 from proof bytes2int-int2bytes-len-eq (previous step)

b2i(by0) = i + 1, 255 * i + band(b2i(by), 255) ≤ 0, ~1 ≤ i, ~129 < i * 256 + band(b2i(by), 255), i * 256 + band(b2i(by), 255) < 0, 256 ≤ abs(band(b2i(by), 255)), ∀ bytes0. # bytes0 < #((by0 + []) + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ by0 = i2b(0), by = i2b(0), b2i(by) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 168:
⊦ ¬ j < 0 → abs(j) = j

Rule argument

seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [band(b2i(by), 255)] rotate: F spec: int-abs inst: name: Abs-pos

Additional information

Used simplifier rules: ⊦ 0 ≤ i → ¬ band(i, j) < 0;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ ¬ 256 ≤ band(i, 255);% ⊦ band(i, band(i0, j)) = band(band(i, i0), j);% ⊦ band(i, j) = band(j, i); Used terms: band(b2i(by), 255)