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Proof step 1 from proof band-min (conclusion)

⊦ i0 ≤ ~(2 ^ n→i(# int2bits(i))) ∧ # int2bits(i) = # int2bits(j) ∧ i ≤ 0 ∧ j ≤ 0 → ¬ band(i, j) < i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# int2bits(i) = # int2bits(j), band(i, j) < i0, i ≤ 0, j ≤ 0, i0 + 2 ^ n→i(# int2bits(j)) ≤ 0 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward)% ⊦ i ≤ ~ j ↔ i + j ≤ 0;