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Proof step 46 from proof shiftzero-pos (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 47:
# int2bits(i) ≠ i→n(j), # int2bits(i) < n, 0 ≤ i, i→n(j) ≤ # int2bits(i), i→n(j) < n ⊦ bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i))) = bits2int(mklist(false, i→n(j)) + firstn(# int2bits(i) - i→n(j), int2bits(i))), # int2bits(i) ≠ i→n(j) ∧ ¬ firstn(# int2bits(i) - i→n(j), int2bits(i)).first
Proof step 50:
# int2bits(i) < n, 0 ≤ i, i→n(j) ≤ # int2bits(i), i→n(j) < n ⊦ # int2bits(i) ≠ i→n(j), bits2int(firstn(n, mklist(false, i→n(j)) + mklist(false, n - # int2bits(i)) + int2bits(i))) = bits2int(mklist(false, i→n(j)) + firstn(# int2bits(i) - i→n(j), int2bits(i))), # int2bits(i) ≠ i→n(j) ∧ ¬ firstn(# int2bits(i) - i→n(j), int2bits(i)).first

Rule argument

fma: # int2bits(i) ≠ i→n(j)

Additional information

Used formulas: # int2bits(i) ≠ i→n(j)