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Proof step 46 from proof validref-putrkvs (previous step)

sk .fs = mkfs(class, ty0, fieldvar), validval(str, val, st[r0 -- _type] .type .type, st), validref(str, r, ty, st), validvals(str, rkvs0, st), is_indexkey(sk), is_referencevalue(val), ∀ str, r, ty, st. validref(str, r, ty, st) ∧ validvals(str, rkvs0, st) → validref(str, r, ty, st[rkvs0]) ⊦ validref(str, r, ty, st[r0 -- sk, val]), validref(str, r, ty, st[r0 -- sk, val][rkvs0]), 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 45:
val = refval(r1), sk .fs = mkfs(class, ty0, fieldvar), validval(str, val, st[r0 -- _type] .type .type, st), validref(str, r, ty, st), validvals(str, rkvs0, st), is_indexkey(sk), is_referencevalue(val), ∀ str, r, ty, st. validref(str, r, ty, st) ∧ validvals(str, rkvs0, st) → validref(str, r, ty, st[rkvs0]) ⊦ validref(str, r, ty, st[r0 -- sk, val]), validref(str, r, ty, st[r0 -- sk, val][rkvs0]), validref(str, r1, st[r0 -- _type] .type .type, st) ∧ r0 ≠ jvmref ∧ is_arraytype(st[r0 -- _type] .type) ∧ (r1 = jvmref → is_reftype(st[r0 -- _type] .type .type))

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)]]