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Proof step 7 from proof no-leading-zero-01 (previous step)

int2bytes(i) = i2b(0) ' + by ' + bytes, i2b(0) ∈ int2bytes(i), 0 ≤ b2i(by), i ≤ 255, ∀ bytes, by, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
127 < i, i ≤ 255 ⊦ int2bytes(i) = i2b(0) ' + i2b(i - 256) '
Proof step 9:
¬(127 < i ∧ i ≤ 255), int2bytes(i) = i2b(0) ' + by ' + bytes, i2b(0) ∈ int2bytes(i), 0 ≤ b2i(by), i ≤ 255, ∀ bytes, by, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦
Proof step 48:
127 < i ∧ i ≤ 255, i2b(0) ' + i2b(i - 256) ' = i2b(0) ' + by ' + bytes, i2b(0) ∈ i2b(0) ' + i2b(i - 256) ', 0 ≤ b2i(by), i ≤ 255, ∀ bytes, by, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦

Rule argument

name: int2bytes-le255 rotate: F subst: [i] → [i]

Additional information

Used terms: i