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Proof step 51 from proof intshiftrzero-prop-01 (previous step)

32 ≤ # mklist(false, i→n(band(j, 31))) + # fillsgn(32, int2bits(i)) ∧ # mklist(false, i→n(band(j, 31))) ≤ 32, 2 * 2 ^ (31 - band(j, 31)) = 2 ^ (32 - band(j, 31)), # int2bits(i) ≤ 32, ~2147483648 ≤ i, i < 0, band(j, 31) ≤ 31, 0 < band(j, 31) ⊦ band(j, 31) = 0, bits2int(mklist(false, i→n(band(j, 31))) + firstn(32 - # mklist(false, i→n(band(j, 31))), fillsgn(32, int2bits(i)))) = bits2int(firstn(32, mklist(true, i→n(band(j, 31))) + fillsgn(32, int2bits(i)))) + 2 ^ (32 - band(j, 31)), false ∈ int2bits(31).rest

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: band-commutativity: ⊦ band(i, j) = band(j, i);%j0 ≠ 0, j ≤ j0 ⊦ i ≤ (* j) → i ≤ (* j0);%0 ≤ i ⊦ i→n(i) ≤ (* m) ↔ i ≤ n→i(m);% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m ≤ m + n;% ⊦ # bits ≤ n → # fillsgn(n, bits) = n;% ⊦ # mklist(boolvar, n) = n;