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Proof step 9 from proof validref-put-array-refval-03 (previous step)

is_arraytype(st[r0 -- _type] .type), validref(str, val .refval, st[r0 -- _type] .type .type, st), is_referencevalue(val), is_indexkey(sk), validref(str, r, ty, st), val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type) ⊦ r0 = jvmref, validref(str, r, ty, st[r0 -- sk, val])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
val = refval(r1), is_arraytype(st[r0 -- _type] .type), validref(str, r1, st[r0 -- _type] .type .type, st), is_referencevalue(val), is_indexkey(sk), validref(str, r, ty, st), r1 = jvmref → is_reftype(st[r0 -- _type] .type .type) ⊦ r0 = jvmref, validref(str, r, ty, st[r0 -- sk, val])

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [val, r1] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (val, r1)]]