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Proof step 8 from proof band-011x-neg-03 (previous step)

j ≤ 0, 0 ≤ i, j ≤ i + 1 ⊦ band(~ j, i) = (i + 1 - j) % (i + 1), false ∈ int2bits(i).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % (i + 1)
Proof step 10:
0 ≤ ~ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i, j ≤ 0, 0 ≤ i, j ≤ i + 1 ⊦ ~ j % (i + 1) = (i + 1 - j) % (i + 1), false ∈ int2bits(i).rest

Rule argument

name: band-011x-pos-02 rotate: F subst: [i, j] → [i, ~ j]

Additional information

Used simplifier rules: ⊦ i ≤ ~ j ↔ i + j ≤ 0;% ⊦ i + 0 = i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false); Used terms: i, ~ j