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Proof step 58 from proof setInt-theorem (previous step)

i >> 8 = b2i(i2b(i >> 8)), fillsgn(3, i2b(i >> 8) ') = by ' + by0 ' + by1 ', 0 ≤ i >> 8, 128 ≤ i, 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

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] → [i2b(i >> 8) ', 3] flags: rewrite, current

Additional information

Used simplifier rules: bytes2int-one: ⊦ bytes2int(by ') = b2i(by);%len-02: ⊦ # by ' = 0 +1; from specification list[bytelist]%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs Used terms: i2b(i >> 8) ', 3