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Proof step 16 from proof okarray-addarray (previous step)

∀ val. val ∈ vals → okval(val, ty) ⊦ is_arrayref(r, n→i(# vals), addarray(r, ty, vals, st)), r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st)
Proof step 15:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)

Rule argument

[speclemmaarg: ,is_arrayref(r, i, st) ↔ (∀ j. 0 ≤ j ∧ j < i → r -- j ' ∈ st) ,[st, i, r] → [addarray(r, ty, vals, st), n→i(# vals), r] ,F ,storearrays , ,is_arrayref ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (addarray(r, ty, vals, st), n→i(# vals), r)]]