[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 99 from proof setInt-theorem (previous step)

2 = # int2bytes(i >> 8), fillsgn(3, int2bytes(i >> 8)) = by ' + by0 ' + by1 ', 128 ≤ i, 0 ≤ i >> 8, 0 < i, 0 ≤ i ⊦ i = b2i(i2b(i)), by = i2b(i >> 24) ∧ by0 = i2b(i >> 16) ∧ by1 = i2b(i >> 8)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 100:
⊦ # bytes < n ∧ 0 ≤ bytes2int(bytes) → fillsgn(n, bytes) = mklist(i2b(0), n - # bytes) + bytes
Proof step 101:
# int2bytes(i >> 8) < 3 ∧ 0 ≤ bytes2int(int2bytes(i >> 8)), 2 = # int2bytes(i >> 8), mklist(i2b(0), 3 - # int2bytes(i >> 8)) + int2bytes(i >> 8) = by ' + by0 ' + by1 ', 128 ≤ i, 0 ≤ i >> 8, 0 < i, 0 ≤ i ⊦ i = b2i(i2b(i)), by = i2b(i >> 24) ∧ by0 = i2b(i >> 16) ∧ by1 = i2b(i >> 8)

Rule argument

spec: bytes inst: name: fillsgn-pos seq: ⊦ # bytes < n ∧ 0 ≤ bytes2int(bytes) → fillsgn(n, bytes) = mklist(i2b(0), n - # bytes) + bytes subst: [bytes, n] → [int2bytes(i >> 8), 3] flags: rewrite, current

Additional information

Used simplifier rules: int2int: ⊦ bytes2int(int2bytes(i)) = i;%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat Used terms: int2bytes(i >> 8), 3