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Proof step 25 from proof band-min-01 (previous step)

# bitsand(int2bits(i), int2bits(j)) ≤ # int2bits(i) ∧ bitsand(int2bits(i), int2bits(j)) ≠ [] → ¬ 2 ^ n→i(# int2bits(i)) + bits2int(bitsand(int2bits(i), int2bits(j))) < 0, bits2int(bitsand(int2bits(i), int2bits(j))) < i0, i0 + 2 ^ n→i(# int2bits(i)) ≤ 0, i0 + 2 ^ n→i(# int2bits(j)) ≤ 0, i < 0, j < 0, # 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)) ≠ [];% ⊦ # bits = 0 ↔ bits = [];% ⊦ m ≤ n ∧ n < n0 → m < n0; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j ≤ i0 + j ↔ i ≤ i0;% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ ¬ m ≤ n ↔ n < m;