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Proof step 10 from proof same-subclasses-array-forward (previous step)

st[r -- i '] = refval(r0), 0 < st[r -- _length] .intval, 0 ≤ i, has_classtype(st[r0 -- _type] .type), i < st[r -- _length] .intval, same-subclasses(st[r -- _type] .type .jtelemtype .class, str, str0), is_array(str, r, st), is_array(str0, r, st), st[r0 -- _type] .type ≤ st[r -- _type] .type .type, ∀ class0. contains(str0, mkclasstype(st[r -- _type] .type .jtelemtype .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r0 = jvmref, contains(str0, mkclasstype(st[r -- _type] .type .jtelemtype .class), st[r0 -- _type] .type .jtelemtype), has_classtype(st[r -- _type] .type), junkref(str0, r0, st), same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class)) → same-subclasses(class, str, str0))

User applied rule insert elim lemma

And closed the goal!

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[r -- _type] .type, ty] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_arraytype (st[r -- _type] .type) → ¬ is_array(str, r, st)], [CSIMPSEQ : ⊦ ¬ is_arraytype(ty) → ty .jtelemtype = ty], [CSIMPSEQ : ⊦ is_arraytype(ty) → ty .jtelemtype = ty .type .jtelemtype], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ has_classtype(mkarraytype(ty)) ↔ has_classtype(ty)], [CSIMPSEQ : ⊦ ¬ has_classtype(ty) → (ty0 ≤ ty ↔ ty0 = ty)], [CSIMPSEQ : ⊦ has_classtype(ty) → mkclasstype (ty .jtelemtype .class) = ty .jtelemtype], [CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r -- _type] .type, ty)]]