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Proof step 13 from proof intshiftrsign-rec-pos (previous step)

i0 < 31, 0 ≤ i, 0 ≤ i0, i ≤ 1 ⊦ bits2int(sublist(0, # int2bits(i), mklist(false, i→n(band(i0 + 1, 31))) + int2bits(i))) = bits2int(sublist(0, # int2bits(i / 2), mklist(false, i→n(band(i0, 31))) + int2bits(i / 2)))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: band-011x-pos-02 rotate: F subst: [i, j] → [31, i0 + 1]

Additional information

Used simplifier rules: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = 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 ';% ⊦ (boolvar ' + bits).rest = bits;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0; Used terms: 31, i0 + 1