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Proof step 1 from proof band-011x-pos-02 (conclusion)

⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % (i + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % 2 ^ n→i(# int2bits(i) - 1)
Proof step 3:
0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i ⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → j % 2 ^ n→i(# int2bits(i) - 1) = j % (i + 1)

Rule argument

name: band-011x-pos-01 rotate: F subst: [i, j] → [i, j]

Additional information

Used simplifier rules: band-011x-pos-01: ⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % 2 ^ n→i(# int2bits(i) - 1);%band-associativity: ⊦ band(i, band(i0, j)) = band(band(i, i0), j);%band-commutativity: ⊦ band(i, j) = band(j, i);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: i, j