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Proof step 1 from proof precise-Sep (conclusion)

∀ a. a ∈ s → precise(aP(a)) ⊦ precise(aP ⊗_ s)

User applied rule induction

And obtained the following new goals

Proof step 2:
∀ a. a ∈ s → precise(aP(a)), ∀ s0, aP. # s0 < # s → (∀ a. a ∈ s0 → precise(aP(a))) → precise(aP ⊗_ s0) ⊦ precise(aP ⊗_ s)

Rule argument

indvar: # s wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: # s