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Proof step 47 from proof int2bytes-leading-zeros (previous step)

int2bytes(i % 256) = bytes0 + i2b(0) ', b2i(i2b(i / 256)) = 0, i2b(0) ∈ int2bytes(i % 256), 0 < i, 0 ≤ i, 255 < i, i / 256 ≤ 127, ∀ bytes, i0. i→n(i0) < i→n(i) → int2bytes(i0) = i2b(0) ' + i2b(0) ' + bytes ∧ 0 ≤ i0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ ~128 ≤ i ∧ i ≤ 127 → b2i(i2b(i)) = i

Rule argument

seq: ⊦ ~128 ≤ i ∧ i ≤ 127 → b2i(i2b(i)) = i subst: [i] → [i / 256] rotate: F spec: byte inst: name: bib-in-01

Additional information

Used simplifier rules: j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0);% ⊦ i < 0 ∧ 0 ≤ j → ¬ j < i;% ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 0 < i ∧ 0 < j → (i / j = 0 ↔ i < j);%0 < j ⊦ 0 ≤ i ∧ i < j → i % (* j) = i;%0 < j ⊦ 0 ≤ i ∧ i < j → i / (* j) = 0;%i + 1 = i0 ⊦ j < (* i0) → ¬ (* i) < j; Used terms: i / 256