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Proof step 54 from proof setInt-theorem (previous step)

fillsgn(3, i2b(i >> 8) ') = by ' + by0 ' + by1 ', i >> 8 = b2i(i2b(i >> 8)), i < ~128 ∨ 128 ≤ i ⊦ i = b2i(i2b(i)), by = i2b(i >> 24) ∧ by0 = i2b(i >> 16) ∧ by1 = i2b(b2i(i2b(i >> 8)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
fillsgn(3, i2b(i >> 8) ') = by ' + by0 ' + by1 ', i >> 8 = b2i(i2b(i >> 8)), i < ~128 ∨ 128 ≤ i ⊦ i = b2i(i2b(i)), by = i2b(i >> 24) ∧ by0 = i2b(i >> 16) ∧ by1 = i2b(i >> 8)

Rule argument

Additional information

Used simplifier rules: in-17: ⊦ by ∈ by0 ' ↔ by = by0; from specification list[bytelist]%in-append: ⊦ by ∈ bytes + bytes0 ↔ ¬ ¬(by ∈ bytes ∨ by ∈ bytes0); from specification list[bytelist]%in-14: ⊦ by ' + bytes = bytes0 → by ∈ bytes0; (forward) from specification list[bytelist]%a: ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; from specification list[bytelist]%in-15: ⊦ bytes + by ' = bytes0 → by ∈ bytes0; (forward) from specification list[bytelist]%ibi: ⊦ i2b(b2i(by)) = by; from specification byte