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Proof step 16 from proof no-leading-zero-04 (previous step)

int2bytes(i / 256 - 1) + i2b(i % 256) ' = i2b(~1) ' + by ' + bytes, i < 0, i < ~256, b2i(by) < 0, i2b(i % 256) ∈ bytes, ∀ 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 apply induction

And obtained the following new goals

Proof step 17:
int2bytes(i / 256 - 1) + i2b(i % 256) ' = i2b(~1) ' + by ' + bytes, i < 0, i < ~256, b2i(by) < 0, i2b(i % 256) ∈ bytes, ∀ bytes, by, i0. i→n(i0) < i→n(i) → true → b2i(by) < 0 → int2bytes(i0) ≠ i2b(~1) ' + by ' + bytes ⊦ i→n(i / 256 - 1) < i→n(i), bytes = [], i % 256 = 0, ¬ i2b(~1) ∈ int2bytes(i / 256 - 1) ∧ i2b(~1) ≠ i2b(i % 256)
Proof step 32:
b2i(by) < 0 → int2bytes(i / 256 - 1) ≠ i2b(~1) ' + by ' + bytes.butlast, int2bytes(i / 256 - 1) + i2b(i % 256) ' = i2b(~1) ' + by ' + bytes, i < 0, i < ~256, b2i(by) < 0, i2b(i % 256) ∈ bytes, ∀ 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)

Rule argument

subst: [bytes, by, i0] → [bytes.butlast, by, i / 256 - 1]

Additional information

Used terms: bytes.butlast, by, i / 256 - 1