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Proof step 14 from proof band-011x-neg-03 (previous step)

0 ≤ i, 0 < j ⊦ (1 - j) % (i + 1) + i = band(i + 1 - j, 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 + 1 - j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i), 0 ≤ i, 0 < j ⊦ (1 - j) % (i + 1) + i = band(i + 1 - j, i), false ∈ int2bits(i).rest
Proof step 29:
0 ≤ i + 1 - j ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i, 0 ≤ i, 0 < j ⊦ (1 - j) % (i + 1) + i = (i + 1 - j) % (i + 1), false ∈ int2bits(i).rest

Rule argument

name: band-011x-pos-02 rotate: F subst: [i, j] → [i, i + 1 - j]

Additional information

Used terms: i, i + 1 - j