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Proof step 31 from proof int2bits-neg-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ boolvar → (bits + boolvar ')+1 = bits +1 + false
Proof step 33:
¬ ~1 ≠ (2 ^ n→i(# int2bits(~ j)) + j) % 2, sgn((bitsinvert(uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2))) + (~1 ≠ (2 ^ n→i(# int2bits(~ j)) + j) % 2)')+1) = boolvar ', j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0 ⊦ ~1 = 2 ^ n→i(# int2bits(~ j)) + j
Proof step 39:
~1 ≠ (2 ^ n→i(# int2bits(~ j)) + j) % 2, sgn(bitsinvert(uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2))) +1 + false) = boolvar ', j < 0, 2 ^ n→i(# int2bits(~ j)) + j < 0 ⊦ ~1 = 2 ^ n→i(# int2bits(~ j)) + j

Rule argument

seq: ⊦ boolvar → (bits + boolvar ')+1 = bits +1 + false subst: [boolvar, bits] → [~1 ≠ (2 ^ n→i(# int2bits(~ j)) + j) % 2, bitsinvert(uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2)))] rotate: F spec: bitopsaux inst: name: succ-rec-01

Additional information

Used terms: ~1 ≠ (2 ^ n→i(# int2bits(~ j)) + j) % 2, bitsinvert(uint2bits(~((2 ^ n→i(# int2bits(~ j)) + j) / 2)))