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Proof step 10 from proof validref-put-array-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ is_indexkey(sk) ↔ (∃ i. sk = i ')
Proof step 9:
∃ i. sk = i ', validref(str, r, ty, st), ¬ is_referencevalue(val) → okval(val, st[r0 -- _type] .type .type), is_referencevalue(val) → validref(str, val .refval, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (val .refval = jvmref → is_reftype(st[r0 -- _type] .type .type)) ⊦ validref(str, r, ty, st[r0 -- sk, val])

Rule argument

[speclemmaarg: ,is_indexkey(sk) ↔ (∃ i. sk = i ') ,[sk] → [sk] ,F ,storekey , ,ex-04 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk)]]