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Proof step 53 from proof hasSharing-pathex (previous step)

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

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, refs1 + r0 ', r, str] ,F ,cyclic , ,validrefs-array ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r -- _type] .type, refs1 + r0 ', r, str)]]