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Proof step 8 from proof no-leading-zero-04 (previous step)

int2bytes(i) = i2b(~1) ' + by ' + bytes, b2i(by) < 0, i2b(~1) ∈ int2bytes(i), i < ~256, i < 0, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ i % 256 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i < ~256 ∧ i % 256 ≠ 0 → int2bytes(i) = int2bytes(i / 256 - 1) + int2bytes(i % 256).last '
Proof step 10:
i < ~256 ∧ i % 256 ≠ 0, int2bytes(i / 256 - 1) + int2bytes(i % 256).last ' = i2b(~1) ' + by ' + bytes, b2i(by) < 0, i2b(~1) ∈ int2bytes(i / 256 - 1) + int2bytes(i % 256).last ', i < ~256, i < 0, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ i % 256 = 0

Rule argument

name: int2bytes-rec-neg-256-01 rotate: F subst: [i] → [i]

Additional information

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