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Proof step 9 from proof in-list-subset (previous step)

st ⊆ st0, r -- sk ∈ st, st[r -- sk] .refval -- sks0 ∈ st, r -- sk ∈ st0, r ∈ st, r ∈ st0, st[r -- sk] .refval -- sks0 ∈ st0, ∀ r0, st1, st2. r0 -- sks0 ∈ st1 ∧ st1 ⊆ st2 → r0 -- sks0 ∈ st2 ⊦ sks0 = [], st0[r -- sk] .refval -- sks0 ∈ st0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,rk ∈ st ∧ ¬ rk ∈ st0 → ¬ st ⊆ st0 ,[rk, st, st0] → [r -- sk, st, st0] ,F ,store ,javastore ,superset-elem-in-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r -- sk, st, st0)]]