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Proof step 2 from proof band-011x-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i → band(j, i) = (j + 1) % (i + 1) + i
Proof step 4:
¬(~ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i), 0 ≤ i ⊦ band(~ j, i) = band(i + 1 - j, i), false ∈ int2bits(i).rest
Proof step 13:
~ j < 0 ∧ ¬ false ∈ int2bits(i).rest ∧ 0 ≤ i, 0 ≤ i ⊦ (~ j + 1) % (i + 1) + i = band(i + 1 - j, i), false ∈ int2bits(i).rest

Rule argument

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

Additional information

Used terms: i, ~ j