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Proof step 16 from proof setInt-theorem (previous step)

fillsgn(4, i2b(i) ') = by ' + by0 ' + by1 ' + by2 ', by ∈ fillsgn(4, i2b(i) '), by2 ∈ fillsgn(4, i2b(i) ') ⊦ by = i2b(b2i(i2b(i)) >> 24) ∧ by0 = i2b(b2i(i2b(i)) >> 16) ∧ by1 = i2b(b2i(i2b(i)) >> 8) ∧ by2 = i2b(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ # bytes < n ∧ bytes2int(bytes) < 0 → fillsgn(n, bytes) = mklist(i2b(~1), n - # bytes) + bytes
Proof step 18:
¬(# i2b(i) ' < 4 ∧ bytes2int(i2b(i) ') < 0), fillsgn(4, i2b(i) ') = by ' + by0 ' + by1 ' + by2 ', by ∈ fillsgn(4, i2b(i) '), by2 ∈ fillsgn(4, i2b(i) ') ⊦ by = i2b(b2i(i2b(i)) >> 24) ∧ by0 = i2b(b2i(i2b(i)) >> 16) ∧ by1 = i2b(b2i(i2b(i)) >> 8) ∧ by2 = i2b(i)
Proof step 30:
# i2b(i) ' < 4 ∧ bytes2int(i2b(i) ') < 0, mklist(i2b(~1), 4 - # i2b(i) ') + i2b(i) ' = by ' + by0 ' + by1 ' + by2 ', by ∈ mklist(i2b(~1), 4 - # i2b(i) ') + i2b(i) ', by2 ∈ mklist(i2b(~1), 4 - # i2b(i) ') + i2b(i) ' ⊦ by = i2b(b2i(i2b(i)) >> 24) ∧ by0 = i2b(b2i(i2b(i)) >> 16) ∧ by1 = i2b(b2i(i2b(i)) >> 8) ∧ by2 = i2b(i)

Rule argument

spec: bytes inst: name: fillsgn-neg seq: ⊦ # bytes < n ∧ bytes2int(bytes) < 0 → fillsgn(n, bytes) = mklist(i2b(~1), n - # bytes) + bytes subst: [bytes, n] → [i2b(i) ', 4] flags: rewrite, current

Additional information

Used terms: i2b(i) ', 4