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Proof step 19 from proof band-min-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: and-notempty-09: ⊦ bitsand(int2bits(i), int2bits(i0)) ≠ [];% ⊦ m +1 = m + 1;% ⊦ # bits = 0 ↔ bits = [];% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ int2bits(j) ≠ [];