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Proof step 17 from proof band-011x-eq (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = (j + 1) % (i + 1) + i
Proof step 19:
i - j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i, 0 ≤ i, 0 ≤ j, i < j, 0 < j ⊦ (((i - j) + 1) % (i + 1) + i) + j % (i + 1) = i, false ∈ int2bits(i).rest

Rule argument

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

Additional information

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