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Proof step 8 from proof byte-mult (previous step)

¬(i * 256 < 0 ∧ ~128 ≤ (i * 256) % 256), ¬(~128 ≤ i * 256 ∧ i * 256 ≤ 127) ⊦ b2i(i2b(i * 256)) = b2i(i2b(0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 ≤ i ∧ i % 256 ≤ 127 → b2i(i2b(i)) = i % 256

Rule argument

name: bib-pos-low rotate: F subst: [i] → [i * 256]

Additional information

Used simplifier rules: byte: ⊦ b2i(i2b(0)) = 0;%byte: ⊦ b2i(i2b(0)) = 0;% ⊦ 0 < i ∧ j < 0 → ((* j) ≤ (* i) * i0 ↔ j / i ≤ i0);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 ≤ (* j) ↔ i0 ≤ j / i);% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ ¬ i < j ↔ j ≤ i;%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: i * 256