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Proof step 5 from proof band-011x-neg (previous step)

j < 0, 0 ≤ i, j < i ⊦ (j + 1) % 2 ^ i + 2 ^ i = 1 + bits2int(bitsand(false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1)))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits)
Proof step 7:
¬ ( ¬ bitsand(false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1)).first ∧ bitsand(false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1)) ≠ []), j < 0, 0 ≤ i, j < i ⊦ (j + 1) % 2 ^ i + 2 ^ i = 1 + bits2int(bitsand(false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1)))
Proof step 15:
¬ bitsand(false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1)).first ∧ bitsand(false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1)) ≠ [], j < 0, 0 ≤ i, j < i ⊦ (j + 1) % 2 ^ i + 2 ^ i = 1 + bits2uint(bitsand(false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1)))

Rule argument

seq: ⊦ ¬ bits.first ∧ bits ≠ [] → bits2int(bits) = bits2uint(bits) subst: [bits] → [bitsand (false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1))] rotate: F spec: int2bits inst: name: bits2int-pos-02

Additional information

Used terms: bitsand (false ' + mklist(true, i→n(i)), sgn(bitsinvert(uint2bits(~ j)) +1))