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Proof step 73 from proof validrefs-subset-equiv (previous step)

st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, r -- i ' ∈ st, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st0), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, st ⊆ st0, is_array(str, r, st), 0 ≤ i, r ∈ st, r -- _length ∈ st, r -- _type ∈ st, junkref(str, r0, st), ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), junkref(str, r, st)

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, r, str] ,F ,junkrefs , ,junkref-array ]

Additional information

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