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Proof step 14 from proof band-011x-eq (previous step)

0 ≤ i, 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 15:
⊦ 0 ≤ j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = j % (i + 1)
Proof step 16:
¬(0 ≤ i - j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i), 0 ≤ i, 0 ≤ j ⊦ band(i - j, i) + j % (i + 1) = i, false ∈ int2bits(i).rest
Proof step 25:
0 ≤ i - j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i, 0 ≤ i, 0 ≤ j ⊦ (i - j) % (i + 1) + j % (i + 1) = i, false ∈ int2bits(i).rest

Rule argument

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

Additional information

Used terms: i, i - j