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Proof step 31 from proof validref-putrkvs (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
st[r0 -- _type] .type = mkarraytype(ty1), ty1 = void_type, sk .fs = mkfs(class, ty0, fieldvar), is_arraytype(st[r0 -- _type] .type), is_indexkey(sk), validvals(str, rkvs0, st), validref(str, r, ty, st), ∀ str, r, ty, st. validref(str, r, ty, st) ∧ validvals(str, rkvs0, st) → validref(str, r, ty, st[rkvs0]) ⊦ r0 = jvmref, validref(str, r, ty, st[r0 -- sk, refval(jvmref)][rkvs0]), validref(str, r, ty, st[r0 -- sk, refval(jvmref)])

Rule argument

[speclemmaarg: ,is_arraytype(ty) → (ty0 = ty .type ↔ ty = mkarraytype(ty0)) ,[ty, ty0] → [st[r0 -- _type] .type, ty1] ,T ,javatype , ,elim-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_arraytype(ty) → ( ty0 = ty .type ↔ ty = mkarraytype(ty0))])], [EXTRATERMS : (st[r0 -- _type] .type, ty1)]]