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Proof step 1 from proof band-011x-neg-01 (conclusion)

⊦ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = (j + 1) % 2 ^ n→i(# int2bits(i) - 1) + 2 ^ n→i(# int2bits(i) - 1) - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
0 ≤ i, j < 0 ⊦ (j + 1) % 2 ^ n→i(# int2bits(i) - 1) + 2 ^ n→i(# int2bits(i) - 1) = band(j, i) + 1, false ∈ int2bits(i).rest

Rule argument

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i - j = i0 ↔ i = i0 + j;