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Proof step 4 from proof precise-Sep (previous step)

∀ a. a ∈ s → precise(aP(a)), ∀ s0, aP. # s0 < # s → (∀ a. a ∈ s0 → precise(aP(a))) → precise(aP ⊗_ s0) ⊦ # s = 0, s = ∅, precise(aP ⊗_ s)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2)
Proof step 6:
∀ a. a ∈ s → precise(aP(a)), ∀ s0, aP. # s0 < # s → (∀ a. a ∈ s0 → precise(aP(a))) → precise(aP ⊗_ s0) ⊦ # s = 0, precise(aP ⊗_ s), ∀ a. a ∈ s ↔ a ∈ ∅

Rule argument

spec: set-basic name: Extension seq: ⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2) subst: [s2, s1] → [∅, s] flags: <all paths>

Additional information

Used terms: ∅, s