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Proof step 29 from proof intshiftrsign-rec-pos (previous step)

0 ≤ i0 + 1 ∧ ¬ false ∈ int2bits(31).rest ∧ 0 ≤ 31, i0 < 31, 0 ≤ i, 0 ≤ i0, 1 < i, 0 < i ⊦ bits2int ( sublist(0, # int2bits(i / 2), mklist(false, i→n((i0 + 1) % (31 + 1))) + int2bits(i / 2) + (i % 2 = 1)') + (mklist(false, i→n((i0 + 1) % (31 + 1))) + int2bits(i / 2) + (i % 2 = 1)')[# int2bits(i / 2)] ') = bits2int(sublist(0, # int2bits(i / 2), mklist(false, i→n(band(i0, 31))) + int2bits(i / 2)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
i0 < 31, 0 ≤ i, 0 ≤ i0, 1 < i, 0 < i ⊦ bits2int ( sublist(0, # int2bits(i / 2), mklist(false, i→n((i0 + 1) % 32)) + int2bits(i / 2) + (i % 2 = 1)') + (mklist(false, i→n((i0 + 1) % 32)) + int2bits(i / 2) + (i % 2 = 1)')[# int2bits(i / 2)] ') = bits2int(sublist(0, # int2bits(i / 2), mklist(false, i→n(i0 % 32)) + int2bits(i / 2)))

Rule argument

Additional information

Used simplifier rules: band-011x-pos-01: ⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % 2 ^ n→i(# int2bits(i) - 1);%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;%⊦ ¬ boolvar ∈ boolvar0 ' + bits ↔ ¬(boolvar ↔ boolvar0) ∧ ¬ boolvar ∈ bits;% ⊦ (boolvar ' + bits).rest = bits;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ bits + boolvar = bits + boolvar ';% ⊦ boolvar + boolvar0 = boolvar ' + boolvar0 ';% ⊦ uint2bits(1) = false + true;%1 < i ⊦ uint2bits((* i)) = uint2bits(i / 2) + (i % 2 = 1);%0 ≤ i ⊦ int2bits((* i)) = uint2bits(i);