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Proof step 18 from proof validrefs-lastelem (previous step)

st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- _type] = typeval(mkclasstype(st[r0 -- _type] .type .class)), r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), is_classtype(st[r0 -- _type] .type), is_obj(r0, st[r0 -- _type] .type .class, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), validrefs(str, r1 ', ty0, st), r0 ∈ st ⊦ r0 = jvmref, is_reftype(ty0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
st[r0 -- _type] .type = mkclasstype(class0), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), st[r0 -- _type] = typeval(mkclasstype(class0)), r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), is_classtype(st[r0 -- _type] .type), is_obj(r0, class0, st), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), validrefs(str, r1 ', ty0, st), r0 ∈ st ⊦ r0 = jvmref, is_reftype(ty0)

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [st[r0 -- _type] .type, class0] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (st[r0 -- _type] .type, class0)]]