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Proof step 37 from proof int2bytes-leading-zeros (previous step)

¬ 255 < i / 256, int2bytes(i % 256) = bytes0 + i2b(0) ', int2bytes(i / 256) = i2b(0) ', 255 < i, 0 ≤ i, 0 < i, i2b(0) ∈ int2bytes(i % 256), ∀ bytes, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + i2b(0) ' + bytes ∧ 0 ≤ i0 → false ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
int2bytes(i / 256) = i2b(0) ', int2bytes(i % 256) = bytes0 + i2b(0) ', i / 256 ≤ 255, i2b(0) ∈ int2bytes(i % 256), 0 < i, 0 ≤ i, 255 < i, ∀ bytes, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + i2b(0) ' + bytes ∧ 0 ≤ i0 → false ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (i < i * j ↔ 1 < j);% ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0);% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ ¬ i < j ↔ j ≤ i;