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Proof step 9 from proof is_array-addarray (previous step)

⊦ is_array(str, r, addarray(r, ty, i, st)) ↔ type∃(str, ty) ∧ ¬ i < 0 ∧ r ≠ jvmref ∧ ty .jtelemtype ≠ void_type ∧ ty .jtelemtype ≠ abstract_type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 8:
⊦ type∃(str, (addarray(r, ty, i, st)[r -- _type]) .type) ∧ (addarray(r, ty, i, st)[r -- _type]) .type .jtelemtype ≠ void_type ∧ (addarray(r, ty, i, st)[r -- _type]) .type .jtelemtype ≠ abstract_type ∧ is_array(r, addarray(r, ty, i, st)) ↔ type∃(str, ty) ∧ ¬ i < 0 ∧ r ≠ jvmref ∧ ty .jtelemtype ≠ void_type ∧ ty .jtelemtype ≠ abstract_type

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, i, st), r, str] ,F ,okfuns , ,is-real-array-def ]

Additional information

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