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Proof step 3 from proof band-255-pos (previous step)

⊦ 0 ≤ i → band(i, 2 ^ 8 - 1) = i % 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 ≤ j ∧ 0 ≤ i → band(j, 2 ^ i - 1) = j % 2 ^ i

Rule argument

name: band-011x-pos rotate: F subst: [i, j] → [8, i]

Additional information

Used simplifier rules: band-def: ⊦ band(i, j) = bits2int(bitsand(int2bits(i), int2bits(j)));%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);%0 ≤ i ⊦ int2bits((* i)) = uint2bits(i);%1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);% ⊦ uint2bits(1) = false + true;% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ bits + boolvar = bits + boolvar ';% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: 8, i