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Proof step 1 from proof precise-Sep (conclusion)

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

User applied rule induction

And obtained the following new goals

Proof step 2:
∀ 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)

Rule argument

indvar: # st wfpred: <

Additional information

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