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Proof step 3 from proof band-mod256-pos (previous step)

⊦ 0 ≤ i → band(2 ^ 8 - 1, i % 256) = 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
Proof step 5:
0 ≤ i % 256 ∧ 0 ≤ 8 ⊦ 0 ≤ i → (i % 256) % 2 ^ 8 = i % 256

Rule argument

name: band-011x-pos rotate: F subst: [j, i] → [i % 256, 8]

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%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 ';% ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i % j; Used terms: i % 256, 8