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Proof step 5 from proof int2uint-neg (previous step)

j < 0 ⊦ bits2uint(sgn(bitsinvert(uint2bits(~ j)) +1)) = 2 ^ n→i(# sgn(bitsinvert(uint2bits(~ j)) +1)) + j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
0 < j, true ∈ uint2bits(j).rest.rest ⊦ sgn(bitsinvert(uint2bits(j)) +1) = bitsinvert(uint2bits(j)) +1
Proof step 7:
¬(0 < ~ j ∧ true ∈ uint2bits(~ j).rest.rest), j < 0 ⊦ bits2uint(sgn(bitsinvert(uint2bits(~ j)) +1)) = 2 ^ n→i(# sgn(bitsinvert(uint2bits(~ j)) +1)) + j
Proof step 18:
0 < ~ j ∧ true ∈ uint2bits(~ j).rest.rest, j < 0 ⊦ bits2uint(bitsinvert(uint2bits(~ j)) +1) = 2 ^ n→i(# bitsinvert(uint2bits(~ j)) +1) + j

Rule argument

name: uint2bits-sgn-2pot-01 rotate: F subst: [j] → [~ j]

Additional information

Used terms: ~ j