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Proof step 42 from proof no-leading-zero-04 (previous step)

int2bytes(i) = i2b(~1) ' + by ' + bytes, b2i(by) < 0, i2b(~1) ∈ int2bytes(i), ~128 ≤ i, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ i = ~256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) '
Proof step 44:
¬(~128 ≤ i ∧ i < 128), int2bytes(i) = i2b(~1) ' + by ' + bytes, b2i(by) < 0, i2b(~1) ∈ int2bytes(i), ~128 ≤ i, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ i = ~256

Rule argument

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

Additional information

Used simplifier rules: ⊦ by ' = by0 ' + bytes ↔ by = by0 ∧ bytes = [];% ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ by ' ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: i