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Proof step 8 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)) ⊦ r = jvmref, is_arrayref(r, n→i(# vals), addarray(r, mkclasstype(class), vals, st))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i ≤ n→i(# vals) → is_arrayref(r, i, addarray(r, ty, vals, st))

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-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ n→i(m) ≤ n→i(n) ↔ m ≤ n], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : ⊦ ¬ n < n])], [EXTRATERMS : (st, vals, mkclasstype(class), n→i(# vals), r)]]