[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 int2bytes-rec-pos-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 74:
⊦ # bytes ≥ n → fix(n, bytes) = lastn(n, bytes)
Proof step 75:
¬ # bits2bytes(int2bits(j % 2 ^ (i * 8))) ≥ i→n(i) + 1, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, # int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, 0 < i, 2 ^ (i * 8) ≤ j ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = fix(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, int2bits(j % 2 ^ (i * 8)).rest = []
Proof step 84:
# bits2bytes(int2bits(j % 2 ^ (i * 8))) ≥ i→n(i) + 1, # int2bits(j % 2 ^ (i * 8)) = i→n(i * 8) + 1, # int2bits(j % 2 ^ (i * 8)).rest % 8 = 0, 0 < i, 2 ^ (i * 8) ≤ j ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = lastn(i→n(i) + 1, bits2bytes(int2bits(j % 2 ^ (i * 8)))).rest, int2bits(j % 2 ^ (i * 8)).rest = []

Rule argument

name: fix-longer rotate: F subst: [bytes, n] → [bits2bytes(int2bits(j % 2 ^ (i * 8))), i→n(i) + 1]

Additional information

Used terms: bits2bytes(int2bits(j % 2 ^ (i * 8))), i→n(i) + 1