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Proof step 8 from proof int2bits-sgn-02 (previous step)

j < 0 ⊦ j = 0, j = ~1, sgn(bitsinvert(uint2bits(~ j)) +1 + bits) = sgn(bitsinvert(uint2bits(~ j)) +1) + bits

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ true ∈ bits ∧ false ∈ bits → sgn(bits + bits0) = sgn(bits) + bits0
Proof step 10:
¬(true ∈ bitsinvert(uint2bits(~ j)) +1 ∧ false ∈ bitsinvert(uint2bits(~ j)) +1), j < 0 ⊦ j = 0, j = ~1, sgn(bitsinvert(uint2bits(~ j)) +1 + bits) = sgn(bitsinvert(uint2bits(~ j)) +1) + bits

Rule argument

seq: ⊦ true ∈ bits ∧ false ∈ bits → sgn(bits + bits0) = sgn(bits) + bits0 subst: [bits0, bits] → [bits, bitsinvert(uint2bits(~ j)) +1] rotate: F spec: bitopsaux inst: name: sgn-append-01

Additional information

Used terms: bits, bitsinvert(uint2bits(~ j)) +1