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Proof step 177 from proof bytes2int-int2bytes-len-eq (previous step)

# bytes = 1 + # int2bytes(band(b2i(bytes.last), 255) / 256 + bytes2int(bytes.butlast)), 0 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 255 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 0 ≤ band(b2i(bytes.last), 255), 0 ≤ bytes2int(bytes.butlast), ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = [], # bytes = 1, bytes = int2bytes(band(b2i(bytes.last), 255) / 256 + bytes2int(bytes.butlast)) + int2bytes(band(b2i(bytes.last), 255) % 256).last '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 178:
0 < j, 0 ≤ i, i < j ⊦ i / j = 0
Proof step 179:
0 < 256 ∧ 0 ≤ band(b2i(bytes.last), 255) ∧ band(b2i(bytes.last), 255) < 256, # bytes = 1 + # int2bytes(0 + bytes2int(bytes.butlast)), 0 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 255 < bytes2int(bytes.butlast) * 256 + band(b2i(bytes.last), 255), 0 ≤ band(b2i(bytes.last), 255), 0 ≤ bytes2int(bytes.butlast), ∀ bytes0. # bytes0 < # bytes → true → # bytes0 = # int2bytes(bytes2int(bytes0)) → bytes0 = int2bytes(bytes2int(bytes0)) ⊦ bytes = [], # bytes = 1, bytes = int2bytes(0 + bytes2int(bytes.butlast)) + int2bytes(band(b2i(bytes.last), 255) % 256).last '

Rule argument

seq: 0 < j, 0 ≤ i, i < j ⊦ i / j = 0 subst: [j, i] → [256, band(b2i(bytes.last), 255)] rotate: F spec: int-div inst: name: div-zero

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: 256, band(b2i(bytes.last), 255)