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Proof step 7 from proof size-eq-0 (previous step)

adr ∈ as, ∀ as0. # as0 < # as → true → (0 = as0.size ↔ (∀ adr. adr ∈ as0 → adr.size = 0)) ⊦ # as = 0, 0 = as.size ↔ (∀ adr. adr ∈ as → adr.size = 0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ adr ∈ as ↔ (∃ as0. as = as0 ++ adr ∧ ¬ adr ∈ as0)
Proof step 9:
∃ as0. as = as0 ++ adr ∧ ¬ adr ∈ as0, ∀ as0. # as0 < # as → true → (0 = as0.size ↔ (∀ adr. adr ∈ as0 → adr.size = 0)) ⊦ # as = 0, 0 = as.size ↔ (∀ adr. adr ∈ as → adr.size = 0)

Rule argument

spec: set-basic, inst: address-store name: indef seq: ⊦ adr ∈ as ↔ (∃ as0. as = as0 ++ adr ∧ ¬ adr ∈ as0) subst: [as, adr] → [as, adr] flags: <all paths>

Additional information

Used terms: as, adr