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Proof step 59 from proof hassharing-validrefs-dups (previous step)

hasSharing(r1, st), validrefs(str, r1 ' + refs1, st[r1 -- _type] .type, st), validrefs(str, r ' + r1 ' + refs1, st[r -- _type] .type, st), is_array(str, r, st), ∀ st, str, refs, r0. # (r0 ' + refs) < # (r ' + (r1 + refs1)) → (validrefs(str, r0 ' + refs, st[r0 -- _type] .type, st) → hasSharing(r0, st) ∨ ¬ r0 ∈ refs ∧ ¬ dups(refs)) ⊦ r = jvmref, hasSharing(r, st), r ∈ refs1, ¬ r1 ∈ refs1 ∧ ¬ dups(refs1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st))) ,[st, ty, refs, r, str] → [st, st[r -- _type] .type, r1 ' + refs1, r, str] ,F ,cyclic , ,validrefs-array ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r -- _type] .type, r1 ' + refs1, r, str)]]