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Proof step 50 from proof validrefs-subset-01 (previous step)

st[r0 -- i '] = refval(r), r0 ∈ st, 0 ≤ i, 0 < st[r0 -- _length] .intval, st[r0 -- _type] .type ≤ ty, is_array(str, r0, st), st ⊆ st0, i < st[r0 -- _length] .intval, validrefs(str, r ' + refs, st[r0 -- _type] .type .type, st), r0 -- _type ∈ st, r0 -- _length ∈ st, r0 -- i ' ∈ st, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st1 ⊆ st2 ∧ ¬ junkref(str0, r, st1) → validrefs(str0, r ' + refs, ty0, st2) ⊦ r0 = jvmref, junkref(str, r0, st), validrefs(str, r ' + refs, st[r0 -- _type] .type .type, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , is_array(str, r, st) → ( junkref(str, r, st) ↔ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval ≠ jvmref ∧ ( ¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∨ junkref(str, st[r -- i '] .refval, st)))) ,[st, r, str] → [st, r0, str] ,F ,junkrefs , ,junkref-array ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, str)]]