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Proof step 21 from proof no-leading-zero-04 (previous step)

int2bytes(i / 256 - 1) + i2b(i % 256) ' = i2b(~1) ' + by ' + bytes, i2b(i % 256) ∈ bytes, b2i(by) < 0, i < ~256, i < 0, i / 256 ≤ i + 1, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ i % 256 = 0, bytes = [], ¬ 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 22:
⊦ i < j → (j ≤ i + 1 ↔ j = i + 1)
Proof step 23:
¬ i < i / 256, int2bytes(i / 256 - 1) + i2b(i % 256) ' = i2b(~1) ' + by ' + bytes, i2b(i % 256) ∈ bytes, b2i(by) < 0, i < ~256, i < 0, i / 256 ≤ i + 1, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ i % 256 = 0, bytes = [], ¬ i2b(~1) ∈ int2bytes(i / 256 - 1) ∧ i2b(~1) ≠ i2b(i % 256)
Proof step 26:
i < i / 256, int2bytes(i / 256 - 1) + i2b(i % 256) ' = i2b(~1) ' + by ' + bytes, i2b(i % 256) ∈ bytes, b2i(by) < 0, i < ~256, i < 0, i / 256 = i + 1, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ i % 256 = 0, bytes = [], ¬ i2b(~1) ∈ int2bytes(i / 256 - 1) ∧ i2b(~1) ≠ i2b(i % 256)

Rule argument

seq: ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1) subst: [i, j] → [i, i / 256] rotate: F spec: int-abs inst: name: les

Additional information

Used terms: i, i / 256