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Proof step 2 from proof succ-ex (previous step)

false ∈ bits ⊦ ∃ bits0, bits1. bits +1 = bits0 + true ' + bitsinvert(bits1) ∧ bits = bits0 + false ' + bits1 ∧ ¬ false ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ boolvar ∈ bits ↔ (∃ bits0, bits1. bits = bits0 + boolvar ' + bits1 ∧ ¬ boolvar ∈ bits1)
Proof step 4:
∃ bits0, bits1. bits = bits0 + false ' + bits1 ∧ ¬ false ∈ bits1 ⊦ ∃ bits0, bits1. bits +1 = bits0 + true ' + bitsinvert(bits1) ∧ bits = bits0 + false ' + bits1 ∧ ¬ false ∈ bits1

Rule argument

seq: ⊦ boolvar ∈ bits ↔ (∃ bits0, bits1. bits = bits0 + boolvar ' + bits1 ∧ ¬ boolvar ∈ bits1) subst: [bits, boolvar] → [bits, false] rotate: F spec: list inst: bitlista name: lastoc-rew

Additional information

Used terms: bits, false