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Proof step 6 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, precise(aP ⊗_ s), ∀ a. a ∈ s ↔ a ∈ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
a ∈ s, ∀ a. a ∈ s → precise(aP(a)), ∀ s0, aP. # s0 < # s → (∀ a. a ∈ s0 → precise(aP(a))) → precise(aP ⊗_ s0) ⊦ # s = 0, precise(aP ⊗_ s)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ∈ ∅; (s)