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Proof step 31 from proof shiftzero-pos (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 32:
mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i) = mklist(false, i→n(j) + (n - # int2bits(i))) + int2bits(i), # int2bits(i) < i→n(j), 0 ≤ i, # int2bits(i) < n ⊦ j = 0, bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i))) = 0

Rule argument

fma: mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i) = mklist(false, i→n(j) + (n - # int2bits(i))) + int2bits(i)

Additional information

Used simplifier rules: ⊦ mklist(boolvar, m + n) = mklist(boolvar, m) + mklist(boolvar, n);% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used formulas: mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i) = mklist(false, i→n(j) + (n - # int2bits(i))) + int2bits(i)