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Proof step 29 from proof junkref-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_array(str, r, st) ↔ type∃(str, st[r -- _type] .type) ∧ st[r -- _type] .type .jtelemtype ≠ void_type ∧ st[r -- _type] .type .jtelemtype ≠ abstract_type ∧ is_array(r, st)
Proof step 28:
newref(r, st), is_classtype(ty), class∃(str, ty .class), junkrefs(str, r ' + refs0, mkarraytype(ty), addarray(r, ty, vals, st)), ∀ val. val ∈ vals → ¬ junkref(str, val .refval, st) ∧ is_referencevalue(val) ∧ (val .refval ≠ jvmref → st[val .refval -- _type] .type ≤ ty) ⊦ r = jvmref, type∃(str, (addarray(r, ty, vals, st)[r -- _type]) .type) ∧ (addarray(r, ty, vals, st)[r -- _type]) .type .jtelemtype ≠ void_type ∧ (addarray(r, ty, vals, st)[r -- _type]) .type .jtelemtype ≠ abstract_type ∧ is_array(r, addarray(r, ty, vals, st))

Rule argument

[speclemmaarg: , is_array(str, r, st) ↔ type∃(str, st[r -- _type] .type) ∧ st[r -- _type] .type .jtelemtype ≠ void_type ∧ st[r -- _type] .type .jtelemtype ≠ abstract_type ∧ is_array(r, st) ,[st, r, str] → [addarray(r, ty, vals, st), r, str] ,F ,okfuns , ,is-real-array-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r, ty, vals, st), r, str)]]