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Proof step 54 from proof no-leading-zero-01 (previous step)

int2bytes(i / 256) + int2bytes(i % 256).last ' = i2b(0) ' + by ' + bytes, 0 < i, 0 ≤ b2i(by), 255 < i, ∀ bytes, by, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦ int2bytes(i % 256).last ≠ i2b(0) ∧ int2bytes(i % 256).last ≠ by ∧ ¬ int2bytes(i % 256).last ∈ bytes, ¬ i2b(0) ∈ int2bytes(i / 256) ∧ i2b(0) ≠ int2bytes(i % 256).last

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 55:
bytes ≠ [] ⊦ bytes0 + by ' = bytes ↔ bytes0 = bytes.butlast ∧ by = bytes.last
Proof step 56:
i2b(0) ' + by ' + bytes ≠ [], int2bytes(i / 256) = (i2b(0) ' + by ' + bytes).butlast ∧ int2bytes(i % 256).last = (i2b(0) ' + by ' + bytes).last, 0 < i, 0 ≤ b2i(by), 255 < i, ∀ bytes, by, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + by ' + bytes ∧ 0 ≤ b2i(by) ∧ i2b(0) ∈ int2bytes(i0) → false ⊦ int2bytes(i % 256).last ≠ i2b(0) ∧ int2bytes(i % 256).last ≠ by ∧ ¬ int2bytes(i % 256).last ∈ bytes, ¬ i2b(0) ∈ int2bytes(i / 256) ∧ i2b(0) ≠ int2bytes(i % 256).last

Rule argument

seq: bytes ≠ [] ⊦ bytes0 + by ' = bytes ↔ bytes0 = bytes.butlast ∧ by = bytes.last subst: [bytes, by, bytes0] → [i2b(0) ' + by ' + bytes, int2bytes(i % 256).last, int2bytes(i / 256)] rotate: F spec: list-last inst: bytelist name: splitlasteq

Additional information

Used simplifier rules: ⊦ ¬ bytes + bytes0 ≠ [] ↔ bytes = [] ∧ bytes0 = [];% ⊦ by ' ≠ [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: i2b(0) ' + by ' + bytes, int2bytes(i % 256).last, int2bytes(i / 256)