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

⊦ 0 ≤ i ∧ 127 < i % 256 → band(2 ^ 8 - 1, i % 256 - 256) = i % 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ j < 0 ∧ 0 ≤ i → band(j, 2 ^ i - 1) = (j + 1) % 2 ^ i + 2 ^ i - 1
Proof step 5:
i % 256 - 256 < 0 ∧ 0 ≤ 8 ⊦ 0 ≤ i ∧ 127 < i % 256 → ((i % 256 - 256) + 1) % 2 ^ 8 + 2 ^ 8 - 1 = i % 256

Rule argument

name: band-011x-neg rotate: F subst: [j, i] → [i % 256 - 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 ';% ⊦ i - j < i0 ↔ i < j + i0;% ⊦ 0 < j → i % j < j; Used terms: i % 256 - 256, 8