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Proof step 2 from proof int2bits-neg-04 (previous step)

j < 0 ⊦ int2bits(j) = int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest, ∃ i. 2 ^ i + j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
j < 0, ¬(∃ i. ~(2 ^ i) = j) ⊦ int2bits(j) = int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest
Proof step 4:
¬(j < 0 ∧ ¬(∃ i. ~(2 ^ i) = j)), j < 0 ⊦ int2bits(j) = int2bits(2 ^ n→i(# int2bits(~ j)) + j).rest, ∃ i. 2 ^ i + j = 0

Rule argument

name: int2bits-neg-02 rotate: F subst: [j] → [j]

Additional information

Used simplifier rules: ⊦ i + j = j + i; Used terms: j