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Proof step 8 from proof int2bits-truein (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 9:
⊦ true ∈ bits ↔ (∃ bits0, bits1. bitsinvert(bits) +1 = bitsinvert(bits0) + true ' + bits1 ∧ ¬ true ∈ bits1 ∧ bits = bits0 + true ' + bits1)
Proof step 10:
true ∈ uint2bits(~ j) ↔ (∃ bits0, bits1. bitsinvert(uint2bits(~ j)) +1 = bitsinvert(bits0) + true ' + bits1 ∧ ¬ true ∈ bits1 ∧ uint2bits(~ j) = bits0 + true ' + bits1), j < 0 ⊦ j = 0, true ∈ sgn(bitsinvert(uint2bits(~ j)) +1)

Rule argument

seq: ⊦ true ∈ bits ↔ (∃ bits0, bits1. bitsinvert(bits) +1 = bitsinvert(bits0) + true ' + bits1 ∧ ¬ true ∈ bits1 ∧ bits = bits0 + true ' + bits1) subst: [bits] → [uint2bits(~ j)] rotate: F spec: bitopsaux inst: name: succ-exinv

Additional information

Used terms: uint2bits(~ j)