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Proof step 32 from proof band-min-02 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 2 ^ n→i(# int2bits(i) - 1) + bits2int(bitsand(int2bits(i), int2bits(j))) < 2 ^ n→i(# int2bits(i) - 1) + i0

Additional information

Used simplifier rules: ⊦ i + j < i + i0 ↔ j < i0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used formulas: 2 ^ n→i(# int2bits(i) - 1) + bits2int(bitsand(int2bits(i), int2bits(j))) < 2 ^ n→i(# int2bits(i) - 1) + i0