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Proof step 1 from proof intshiftrsign-zero (conclusion)

⊦ i i>> 0 = i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i i>> j = bits2int(sublist(0, # int2bits(i), mklist(int2bits(i).first, i→n(band(j, 31))) + int2bits(i)))

Rule argument

name: intshiftrsign rotate: F subst: [j, i] → [0, i]

Additional information

Used simplifier rules: band-num: ⊦ band((* i), (* j)) = bits2int(bitsand(int2bits(i), int2bits(j)));%bitsand-zerol: ⊦ bitsand(false ', bits + boolvar ') = false ';%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ int2bits(j).first ↔ j < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ int2bits(0) = false ';%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 ';% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits2int(false ') = 0;% ⊦ mklist(boolvar, 0) = [];% ⊦ [] + bits = bits;% ⊦ sublist(0, # bits, bits) = bits;% ⊦ bits2int(int2bits(i)) = i; Used terms: 0, i