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Proof step 34 from proof intshiftrsign32 (previous step)

# int2bits(i) = n0 + i→n(band(j, 31)), # int2bits(i) = i→n(band(j, 31)) + n2, 32 = n1 + # int2bits(i), 32 = (n2 + n1) + i→n(band(j, 31)), i→n(band(j, 31)) ≤ # int2bits(i), # int2bits(i) ≤ 32, band(j, 31) ≤ 32 ⊦ bits2int(mklist(¬ 0 ≤ i, i→n(band(j, 31))) + sublist(0, n0, int2bits(i))) = bits2int((¬ 0 ≤ i)' + sublist(0, n2, int2bits(i))), band(j, 31) = 0, n2 = 0

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);%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2