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Proof step 42 from proof intshiftrsign32 (previous step)

n0 + i→n(band(j, 31)) = n1 + # int2bits(i), i→n(band(j, 31)) < # int2bits(i), n0 ≤ n1, band(j, 31) ≤ 32, # int2bits(i) ≤ n0 + i→n(band(j, 31)), band(j, 31) < 32 ⊦ bits2int(sublist(0, # int2bits(i), mklist(¬ 0 ≤ i, i→n(band(j, 31))) + int2bits(i))) = bits2int((¬ 0 ≤ i)'), band(j, 31) = 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);%l-01: ⊦ m < m + n ↔ n ≠ 0; from specification nat-basic2%f: ⊦ m < n → n ≠ 0; from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%lep: ⊦ m ≤ m + n; from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat