[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 73 from proof bytes2int-int2bytes-len-eq (previous step)

# bytes1 = # int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256), (bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256 = 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, bytes1 = [], bytes1 + by ' = int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256) + i2b(0) '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 74:
⊦ i % j = 0 ∧ i + i0 < 0 ∧ i0 % j = 0 ∧ i < 0 ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) / j = i / j + i0 / j
Proof step 75:
¬ ( (bytes2int(bytes1) * 256) % 256 = 0 ∧ bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0 ∧ band(b2i(by), 255) % 256 = 0 ∧ bytes2int(bytes1) * 256 < 0 ∧ 0 ≤ band(b2i(by), 255) ∧ 0 < 256), # bytes1 = # int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256), (bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256 = 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, bytes1 = [], bytes1 + by ' = int2bytes((bytes2int(bytes1) * 256 + band(b2i(by), 255)) / 256) + i2b(0) '
Proof step 89:
(bytes2int(bytes1) * 256) % 256 = 0 ∧ bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0 ∧ band(b2i(by), 255) % 256 = 0 ∧ bytes2int(bytes1) * 256 < 0 ∧ 0 ≤ band(b2i(by), 255) ∧ 0 < 256, # bytes1 = # int2bytes((bytes2int(bytes1) * 256) / 256 + band(b2i(by), 255) / 256), (bytes2int(bytes1) * 256 + band(b2i(by), 255)) % 256 = 0, bytes2int(bytes1) * 256 + band(b2i(by), 255) < ~256, bytes2int(bytes1) * 256 + band(b2i(by), 255) < 0, ∀ bytes0. # bytes0 < #(bytes1 + by ') → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes2int(bytes1) * 256 + band(b2i(by), 255) = ~256, bytes1 = [], bytes1 + by ' = int2bytes((bytes2int(bytes1) * 256) / 256 + band(b2i(by), 255) / 256) + i2b(0) '

Rule argument

seq: ⊦ i % j = 0 ∧ i + i0 < 0 ∧ i0 % j = 0 ∧ i < 0 ∧ 0 ≤ i0 ∧ 0 < j → (i + i0) / j = i / j + i0 / j subst: [j, i0, i] → [256, band(b2i(by), 255), bytes2int(bytes1) * 256] rotate: F spec: int-div inst: name: div-add1-negpos-neg

Additional information

Used terms: 256, band(b2i(by), 255), bytes2int(bytes1) * 256