[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 69 from proof int2bytes-rec-pos-any (previous step)

# (mklist(j % 2 ^ (i * 8) < 0, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 2 ^ (i * 8) ≤ j, 0 < i ⊦ (mklist(¬ 0 ≤ j % 2 ^ (i * 8), i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest = [], bits2bytes((mklist(¬ 0 ≤ j % 2 ^ (i * 8), i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ m ≠ 0 → (mklist(boolvar, m) + bits).rest = mklist(boolvar, m -1) + bits
Proof step 71:
¬ i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)) ≠ 0, # (mklist(j % 2 ^ (i * 8) < 0, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 2 ^ (i * 8) ≤ j, 0 < i ⊦ (mklist(¬ 0 ≤ j % 2 ^ (i * 8), i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest = [], bits2bytes((mklist(¬ 0 ≤ j % 2 ^ (i * 8), i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest
Proof step 113:
i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)) ≠ 0, # (mklist(j % 2 ^ (i * 8) < 0, i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8))) + int2bits(j % 2 ^ (i * 8))).rest % 8 = 0, # int2bits(j % 2 ^ (i * 8)) ≤ i→n(i * 8) + 1, 2 ^ (i * 8) ≤ j, 0 < i ⊦ mklist(¬ 0 ≤ j % 2 ^ (i * 8), (i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)))-1) + int2bits(j % 2 ^ (i * 8)) = [], bits2bytes(mklist(¬ 0 ≤ j % 2 ^ (i * 8), (i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)))-1) + int2bits(j % 2 ^ (i * 8))) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest

Rule argument

seq: ⊦ m ≠ 0 → (mklist(boolvar, m) + bits).rest = mklist(boolvar, m -1) + bits subst: [bits, m, boolvar] → [int2bits(j % 2 ^ (i * 8)), i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)), ¬ 0 ≤ j % 2 ^ (i * 8)] rotate: F spec: list-last inst: bitlista name: mk-rest-01

Additional information

Used terms: int2bits(j % 2 ^ (i * 8)), i→n(i * 8) + 1 - # int2bits(j % 2 ^ (i * 8)), ¬ 0 ≤ j % 2 ^ (i * 8)