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Proof step 41 from proof cast-help-comm (previous step)

# int2bits(j) < i→n(i), 1 < i0, 0 < i0, 0 < i, i < i0, i ≤ i0 ⊦ mklist(¬ 0 ≤ j, i→n(i) - # int2bits(j)) + int2bits(j) = [], i = 0, i0 = 0, bits2int(lastn(i→n(i), fillsgn(i→n(i0), int2bits(j)))) = bits2int(lastn(i→n(i0), mklist(¬ 0 ≤ j, (i→n(i0) - i→n(i)) + (i→n(i) - # int2bits(j))) + int2bits(j)))

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: (i→n(i0) - i→n(i)) + (i→n(i) - # int2bits(j)) = i→n(i0) - # int2bits(j)

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ i < j → ¬ j < i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ 1 < i → abs(i) = i;% ⊦ 0 < j → abs(j) = j;% ⊦ i→n(i) ≤ i→n(j) ↔ abs(i) ≤ abs(j);%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1;% ⊦ m < n → ¬ n < m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n = m + n0 ↔ n = n0;% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j);% ⊦ m +1 = m + 1;% ⊦ int2bits(j) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n); Used formulas: (i→n(i0) - i→n(i)) + (i→n(i) - # int2bits(j)) = i→n(i0) - # int2bits(j)