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Proof step 39 from proof shiftzero-pos (previous step)

n ≤ i→n(j) + (n - # int2bits(i)), n ≤ # mklist(false, i→n(j) + (n - # int2bits(i))), # int2bits(i) < i→n(j), 0 ≤ i, # int2bits(i) < n ⊦ j = 0, bits2int(mklist(false, n)) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
# int2bits(i) < i→n(j), 0 ≤ i, # int2bits(i) < n, n ≤ i→n(j) + (n - # int2bits(i)), # int2bits(i) < i→n(j) + (n - # int2bits(i)) ⊦ j = 0, bits2int(mklist(false, n)) = 0, n + i→n(j) = # int2bits(i)

Rule argument

Additional information

Used simplifier rules: ⊦ 0 + m = m;%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;% ⊦ m < n → n ≠ 0; (forward)% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);