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

j < 0, 0 ≤ i ⊦ (i - j) % (i + 1) + (j + 1) % 2 ^ n→i(# int2bits(i) - 1) + 2 ^ n→i(# int2bits(i) - 1) = i + 1, false ∈ int2bits(i).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ false ∈ int2bits(j).rest ↔ ¬(∃ i. j = 2 ^ i - 1)
Proof step 10:
j < 0, 0 ≤ i ⊦ (i - j) % (i + 1) + (j + 1) % 2 ^ n→i(# int2bits(i) - 1) + 2 ^ n→i(# int2bits(i) - 1) = i + 1, ∀ i0. i ≠ 2 ^ i0 - 1

Rule argument

seq: ⊦ false ∈ int2bits(j).rest ↔ ¬(∃ i. j = 2 ^ i - 1) subst: [j] → [i] rotate: F spec: int2bits inst: name: int2bits-falsein-02

Additional information

Used terms: i