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Proof step 10 from proof validrefs-applast-class-null (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] .refval = jvmref, is_reftype(ty0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, refs + r ', ty, st) ⊦ validrefs(str, refs + r ' + jvmref ', ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), r0 = jvmref, is_reftype(ty0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']), validrefs(str, refs + r ', ty, st) ⊦ validrefs(str, refs + r ' + jvmref ', ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- mkfs(class, ty0, fieldvar) '], r0] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) '], r0)]]