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Proof step 2 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) ⊦ precise(aP ⊗_ s)

User applied rule cut formula

And obtained the following new goals

Proof step 3:
∀ a. a ∈ s → precise(aP(a)), ∀ s0, aP. # s0 < # s → (∀ a. a ∈ s0 → precise(aP(a))) → precise(aP ⊗_ s0) ⊦ s = ∅, precise(aP ⊗_ s)

Rule argument

fma: s = ∅

Additional information

Used simplifier rules: Sep-emp: ⊦ aP ⊗_ ∅ = emp;% ⊦ precise(emp); (s) Used formulas: s = ∅