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Proof step 24 from proof no-leading-zero-04 (previous step)

int2bytes(i / 256 - 1) + i2b(i % 256) ' = i2b(~1) ' + by ' + bytes, i / 256 < ~256, i / 256 ≤ i, i < 0, i < ~256, b2i(by) < 0, i2b(i % 256) ∈ bytes, i ≤ ~256, i / 256 ≤ ~256, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ bytes = [], i % 256 = 0, ¬ i2b(~1) ∈ int2bytes(i / 256 - 1) ∧ i2b(~1) ≠ i2b(i % 256)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ i < 0 ∧ 0 < j → (i / j ≤ i ↔ i = 0 ∨ j = 1)

Rule argument

seq: ⊦ i < 0 ∧ 0 < j → (i / j ≤ i ↔ i = 0 ∨ j = 1) subst: [j, i] → [256, i] rotate: F spec: int-div inst: name: div-le-same-neg

Additional information

Used simplifier rules: int2bytes-byte: ~128 ≤ i, i < 128 ⊦ int2bytes((* i)) = i2b(i) ';% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ bytes + bytes0 = bytes + bytes1 ↔ bytes0 = bytes1;% ⊦ by ' = by0 ' + bytes ↔ by = by0 ∧ bytes = [];% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1; Used terms: 256, i