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Proof step 2 from proof precise-Sep (previous step)

∀ a. a ∈ st → precise(adP(a, st[a])), ∀ st0, adP. # st0 < # st → (∀ a. a ∈ st0 → precise(adP(a, st0[a]))) → precise(adP ⊗_ st0) ⊦ precise(adP ⊗_ st)

User applied rule cut formula

And obtained the following new goals

Proof step 3:
∀ a. a ∈ st → precise(adP(a, st[a])), ∀ st0, adP. # st0 < # st → (∀ a. a ∈ st0 → precise(adP(a, st0[a]))) → precise(adP ⊗_ st0) ⊦ st = ∅, precise(adP ⊗_ st)

Rule argument

fma: st = ∅

Additional information

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