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Proof step 10 from proof junkref-addarray-01 (previous step)

newref(r, st), class∃(str, class), junkrefs(str, r ' + refs0, mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)), tdname+∃(str, class), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ mkclasstype(class)) ⊦ is_arrayref(r, n→i(# vals), addarray(r, mkclasstype(class), vals, st)), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i < n→i(# vals) → is_arrayref(r, i, addarray(r, ty, vals, st))
Proof step 9:
¬ n→i(# vals) < n→i(# vals), newref(r, st), class∃(str, class), junkrefs(str, r ' + refs0, mkarraytype(mkclasstype(class)), addarray(r, mkclasstype(class), vals, st)), tdname+∃(str, class), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ mkclasstype(class)) ⊦ is_arrayref(r, n→i(# vals), addarray(r, mkclasstype(class), vals, st)), r = jvmref

Rule argument

[speclemmaarg: ,i < n→i(# vals) → is_arrayref(r, i, addarray(r, ty, vals, st)) ,[st, vals, ty, i, r] → [st, vals, mkclasstype(class), n→i(# vals), r] ,F ,addarray , ,isarray-init-01 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, vals, mkclasstype(class), n→i(# vals), r)]]