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Proof step 9 from proof intshiftrsign-if (previous step)

# int2bits(i) ≤ i→n(band(j, 31)), i < 0 ⊦ bits2int(sublist(0, # int2bits(i), mklist(true, i→n(band(j, 31))) + int2bits(i))) = ~1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n + m ≤ m0 → sublist(n, m, mklist(boolvar, m0) + bits) = mklist(boolvar, m) subst: [bits, m0, boolvar, m, n] → [int2bits(i), i→n(band(j, 31)), true, # int2bits(i), 0] rotate: F spec: list-del inst: bitlista name: sublist-mklist-01

Additional information

Used simplifier rules: ⊦ bits2int(mklist(true, # int2bits(i))) = ~1;% ⊦ 0 + m = m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ [];% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ ¬ i < i; Used terms: int2bits(i), i→n(band(j, 31)), true, # int2bits(i), 0