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Proof step 14 from proof band-min-02 (previous step)

# int2bits(i) < # int2bits(j), bits2int(bitsand(int2bits(i), int2bits(j))) < i0, i0 + 2 ^ (n→i(# int2bits(i)) - 1) ≤ 0, i0 + 2 ^ (n→i(# int2bits(j)) - 1) ≤ 0, i < 0, j < 0 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 15:
⊦ # bits - 1 ≤ n ∧ bits ≠ [] → ¬ 2 ^ n→i(n) + bits2int(bits) < 0
Proof step 16:
# bitsand(int2bits(i), int2bits(j)) - 1 ≤ # int2bits(j) - 1 ∧ bitsand(int2bits(i), int2bits(j)) ≠ [] → ¬ 2 ^ n→i(# int2bits(j) - 1) + bits2int(bitsand(int2bits(i), int2bits(j))) < 0, # int2bits(i) < # int2bits(j), bits2int(bitsand(int2bits(i), int2bits(j))) < i0, i0 + 2 ^ (n→i(# int2bits(i)) - 1) ≤ 0, i0 + 2 ^ (n→i(# int2bits(j)) - 1) ≤ 0, i < 0, j < 0 ⊦

Rule argument

seq: ⊦ # bits - 1 ≤ n ∧ bits ≠ [] → ¬ 2 ^ n→i(n) + bits2int(bits) < 0 subst: [bits, n] → [bitsand(int2bits(i), int2bits(j)), # int2bits(j) - 1] rotate: F spec: int2bits inst: name: bits2int-nls-02

Additional information

Used terms: bitsand(int2bits(i), int2bits(j)), # int2bits(j) - 1