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Proof step 34 from proof same-subclasses-array-forward (previous step)

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

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [st[r -- _type] .type .jtelemtype, class1] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkclasstype(class) = mkclasstype(class0) ↔ class = class0], [CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))], [CSIMPSEQ : ⊦ class ≠ `java.lang.Object' .class → ( ty ≤ mkclasstype(class) ↔ is_classtype(ty) ∧ ty .class ≤ class)], [CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (st[r -- _type] .type .jtelemtype, class1)]]