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Proof step 18 from proof int2bits-neg-03 (previous step)

2 ^ n→i(# int2bits(~ j)) + j < 0, sgn(bitsinvert(uint2bits(abs(2 ^ n→i(# int2bits(~ j)) + j))) +1) = boolvar ', j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ 0 < i ∧ i ≠ 1 → uint2bits(i) = uint2bits(i / 2) + (i % 2 = 1)
Proof step 20:
¬(0 < abs(2 ^ n→i(# int2bits(~ j)) + j) ∧ abs(2 ^ n→i(# int2bits(~ j)) + j) ≠ 1), 2 ^ n→i(# int2bits(~ j)) + j < 0, sgn(bitsinvert(uint2bits(abs(2 ^ n→i(# int2bits(~ j)) + j))) +1) = boolvar ', j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0 ⊦
Proof step 30:
0 < abs(2 ^ n→i(# int2bits(~ j)) + j) ∧ abs(2 ^ n→i(# int2bits(~ j)) + j) ≠ 1, 2 ^ n→i(# int2bits(~ j)) + j < 0, sgn(bitsinvert(uint2bits(abs(2 ^ n→i(# int2bits(~ j)) + j) / 2) + (abs(2 ^ n→i(# int2bits(~ j)) + j) % 2 = 1)) +1) = boolvar ', j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0 ⊦

Rule argument

name: uint2bits-rec-01 rotate: F subst: [i] → [abs(2 ^ n→i(# int2bits(~ j)) + j)]

Additional information

Used terms: abs(2 ^ n→i(# int2bits(~ j)) + j)