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Proof step 21 from proof bits2bits-def (previous step)

true ∈ bits0, 0 < bits2uint(false ' + bitsinvert(bits0) +1) ⊦ sgn(sgn(true ' + bitsinvert(bitsinvert(bits0) +1)) +1) = sgn(true ' + bits0)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 22:
⊦ true ∈ bits ↔ (∃ bits0, bits1. bitsinvert(bits) +1 = bitsinvert(bits0) + true ' + bits1 ∧ ¬ true ∈ bits1 ∧ bits = bits0 + true ' + bits1)
Proof step 23:
true ∈ bits0 ↔ (∃ bits2, bits1. bitsinvert(bits0) +1 = bitsinvert(bits2) + true ' + bits1 ∧ ¬ true ∈ bits1 ∧ bits0 = bits2 + true ' + bits1), true ∈ bits0, 0 < bits2uint(false ' + bitsinvert(bits0) +1) ⊦ sgn(sgn(true ' + bitsinvert(bitsinvert(bits0) +1)) +1) = sgn(true ' + bits0)

Rule argument

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

Additional information

Used terms: bits0