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Proof step 4 from proof is_array-addobj-01 (previous step)

is_array(str, r, addobj(r, class, fis, st)) ⊦ _type ∈ fis

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 2:
¬ _type ∈ fis ⊦ (addobj(r, class1, fis, st)[r -- _type]) = typeval(mkclasstype(class1))
Proof step 3:
⊦ ¬ _type ∈ fis → ¬ is_array(r, addobj(r, class, fis, 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] → [addobj(r, class, fis, st), r, str] ,F ,okfuns , ,is-real-array-def ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPSEQ : ⊦ mkclasstype(class) .jtelemtype = mkclasstype(class)], [CSIMPSEQ : ⊦ mkclasstype(class) ≠ abstract_type], [CSIMPSEQ : ⊦ mkclasstype(class) ≠ void_type], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)])], [EXTRATERMS : (addobj(r, class, fis, st), r, str)]]