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Proof step 13 from proof no-leading-zero-01 (previous step)

int2bytes(i) = i2b(0) ' + by ' + bytes, i2b(0) ∈ int2bytes(i), 0 ≤ b2i(by), i < ~128, i < 0, ∀ 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 14:
⊦ i < ~ 128 → int2bytes(i) = int2bytes((i - 255) / 256) + int2bytes(i % 256).last '
Proof step 15:
i < ~ 128, int2bytes((i - 255) / 256) + int2bytes(i % 256).last ' = i2b(0) ' + by ' + bytes, i2b(0) ∈ int2bytes((i - 255) / 256) + int2bytes(i % 256).last ', 0 ≤ b2i(by), i < ~128, i < 0, ∀ 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-rec255-neg rotate: F subst: [i] → [i]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: i