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Proof step 5 from proof int2bits-rec-neg (previous step)

j < 0 ⊦ j = ~1, sgn(bitsinvert(uint2bits(~ j)) +1) = int2bits((j - 1) / 2) + (~1 = j % 2)'

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i < 0 → int2bits(i) = sgn(bitsinvert(uint2bits(abs(i))) +1)
Proof step 7:
(j - 1) / 2 < 0, j < 0 ⊦ j = ~1, sgn(bitsinvert(uint2bits(~ j)) +1) = sgn(bitsinvert(uint2bits(abs((j - 1) / 2))) +1) + (~1 = j % 2)'

Rule argument

name: int2bits-neg rotate: F subst: [i] → [(j - 1) / 2]

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: (j - 1) / 2