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Proof step 102 from proof setInt-theorem (previous step)

int2bytes(i >> 8) = by0 ' + by1 ', 0 ≤ i, 0 < i, 0 ≤ i >> 8, 128 ≤ i ⊦ i = b2i(i2b(i)), i2b(0) = 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 103:
⊦ i < ~128 ∨ 128 ≤ i → int2bytes(i) = int2bytes(i >> 8) + i2b(i)
Proof step 104:
¬(i >> 8 < ~128 ∨ 128 ≤ i >> 8), int2bytes(i >> 8) = by0 ' + by1 ', 0 ≤ i, 0 < i, 0 ≤ i >> 8, 128 ≤ i ⊦ i = b2i(i2b(i)), i2b(0) = i2b(i >> 24) ∧ by0 = i2b(i >> 16) ∧ by1 = i2b(i >> 8)
Proof step 107:
i >> 8 < ~128 ∨ 128 ≤ i >> 8, int2bytes((i >> 8) >> 8) + i2b(i >> 8) = by0 ' + by1 ', 0 ≤ i, 0 < i, 0 ≤ i >> 8, 128 ≤ i ⊦ i = b2i(i2b(i)), i2b(0) = i2b(i >> 24) ∧ by0 = i2b(i >> 16) ∧ by1 = i2b(i >> 8)

Rule argument

spec: bytes inst: name: int2bytes-rec-shift seq: ⊦ i < ~128 ∨ 128 ≤ i → int2bytes(i) = int2bytes(i >> 8) + i2b(i) subst: [i] → [i >> 8] flags: rewrite, current

Additional information

Used terms: i >> 8