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Proof step 13 from proof band-min-02 (previous step)

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 cut formula

And obtained the following new goals

Proof step 14:
# 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 ⊦
Proof step 25:
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 ⊦ # int2bits(i) < # int2bits(j)

Rule argument

fma: # int2bits(i) < # int2bits(j)

Additional information

Used formulas: # int2bits(i) < # int2bits(j)