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Proof step 8 from proof hassharing-validrefs-dups (previous step)

st[r -- sks] = refval(r), # sks = 1 + # refs1, validrefs(str, r ' + refs1 + r ', st[r -- _type] .type, st), fits(r, sks, st), is_valid_ref(str, r, st), ∀ n. n ≠ 0 ∧ ¬ # sks < n → st[r -- firstn(n, sks)] .refval = (r ' + refs1 + r ')[n], ∀ st, str, refs2, r0. # (r0 ' + refs2) < # (r ' + refs1 + (r + refs)) → (validrefs(str, r0 ' + refs2, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs2 ∧ ¬ dups(refs2)) ⊦ sks = [], r = jvmref, refval(r) = st[r -- (sks + sks)]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , sks ≠ [] ∧ sks0 ≠ [] → st[r -- (sks + sks0)] = st[st[r -- sks] .refval -- sks0] ,[sks0, sks, r, st] → [sks, sks, r, st] ,F ,storefuns , ,lookup-append ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r])], [EXTRATERMS : (sks, sks, r, st)]]