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Proof step 12 from proof precise-Sep (previous step)

precise(adP(a, d)), ∀ a0. a0 ∈ st0[a, d] → precise(adP(a0, st0[a, d][a0])), ∀ st1, adP. # st1 < # st0[a, d] → (∀ a. a ∈ st1 → precise(adP(a, st1[a]))) → precise(adP ⊗_ st1) ⊦ precise(adP ⊗_ st0), precise(adP(a, d) * adP ⊗_ st0), a ∈ st0, ∀ a. a ∈ st0 → precise(adP(a, st0[a]))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
precise(adP(a, d)), a0 ∈ st0, ∀ a0. a0 ∈ st0[a, d] → precise(adP(a0, st0[a, d][a0])), ∀ st1, adP. # st1 < # st0[a, d] → (∀ a. a ∈ st1 → precise(adP(a, st1[a]))) → precise(adP ⊗_ st1) ⊦ precise(adP(a0, st0[a0])), precise(adP(a, d) * adP ⊗_ st0), precise(adP ⊗_ st0), a ∈ st0

Proof step 12 from proof precise-Sep (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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