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Proof step 2 from proof band-011x-is-unsigned-01 (previous step)

abs(j) ≤ 2 ^ n→i(# int2bits(i0) - 2), 0 < i0 ⊦ band(j, i0) = bits2uint(fillsgn(# int2bits(i0) - 1, int2bits(j))), false ∈ int2bits(i0).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ false ∈ int2bits(j).rest ↔ ¬(∃ i. j = 2 ^ i - 1)
Proof step 4:
abs(j) ≤ 2 ^ n→i(# int2bits(i0) - 2), 0 < i0 ⊦ band(j, i0) = bits2uint(fillsgn(# int2bits(i0) - 1, int2bits(j))), ∀ i. i0 ≠ 2 ^ i - 1

Rule argument

seq: ⊦ false ∈ int2bits(j).rest ↔ ¬(∃ i. j = 2 ^ i - 1) subst: [j] → [i0] rotate: F spec: int2bits inst: name: int2bits-falsein-02

Additional information

Used terms: i0