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Proof step 43 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)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ bits ≠ [] ∧ (bits.first ↔ boolvar) → bits2int(mklist(boolvar, n) + bits) = bits2int(bits)
Proof step 45:
¬(firstn(# int2bits(i) - i→n(j), int2bits(i)) ≠ [] ∧ (firstn(# int2bits(i) - i→n(j), int2bits(i)).first ↔ false)), # 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)))
Proof step 69:
firstn(# int2bits(i) - i→n(j), int2bits(i)) ≠ [] ∧ (firstn(# int2bits(i) - i→n(j), int2bits(i)).first ↔ false), # 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(firstn(# int2bits(i) - i→n(j), int2bits(i)))

Rule argument

seq: ⊦ bits ≠ [] ∧ (bits.first ↔ boolvar) → bits2int(mklist(boolvar, n) + bits) = bits2int(bits) subst: [bits, n, boolvar] → [firstn(# int2bits(i) - i→n(j), int2bits(i)), i→n(j), false] rotate: F spec: int2bits inst: name: bits2int-mklist

Additional information

Used terms: firstn(# int2bits(i) - i→n(j), int2bits(i)), i→n(j), false