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Proof step 6 from proof precise-Sep (previous step)

∀ 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(a, d) * adP ⊗_ st0), a ∈ st0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ precise(P0) ∧ precise(P1) → precise(P0 * P1)
Proof step 8:
∀ 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(a, d) * adP ⊗_ st0), a ∈ st0, precise(adP(a, d)) ∧ precise(adP ⊗_ st0)

Rule argument

spec: heap-sep name: precise-sep seq: ⊦ precise(P0) ∧ precise(P1) → precise(P0 * P1) subst: [P1, P0] → [adP ⊗_ st0, adP(a, d)] flags: <all paths>

Additional information

Used terms: adP ⊗_ st0, adP(a, d)