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Proof step 4 from proof Sep-eq (previous step)

(adP ⊗_ st)(H), ∀ a. a ∈ st → adP(a, st[a]) = adP0(a, st[a]) ⊦ (adP0 ⊗_ st)(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
∀ a, H. a ∈ st ∧ adP0(a, st[a])(H) → adP(a, st[a])(H) ⊦ (adP0 ⊗_ st)(H) → (adP ⊗_ st)(H)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: Sep-forall antecedent: ∀ a, H. a ∈ st ∧ adP0(a, st[a])(H) → adP(a, st[a])(H) succedent: (adP0 ⊗_ st)(H) → (adP ⊗_ st)(H) substlist: [adP0, H, st, adP] → [adP, H, st, adP0] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (adP, H, st, adP0)]]