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Proof step 14 from proof validrefs-lastelem (previous step)

st[r0 -- _type] = typeval(mkclasstype(class0)), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), is_obj(r0, class0, st), r0 -- _type ∈ st, r0 ∈ st, validrefs(str, r1 ', ty0, st), is_obj(str, r0, st), class0 ≤ class1 ⊦ r0 = jvmref, is_reftype(ty0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ is_obj(r, class, st) ↔ r ≠ jvmref ∧ (r -- _type) × typeval(mkclasstype(class)) ∈ st ∧ goodfieldsandtypes(r, instfields(class), st)
Proof step 13:
st[r0 -- _type] = typeval(mkclasstype(class0)), st[r0 -- mkfs(class, ty0, fieldvar) '] = refval(r1), mkfs(class, ty0, fieldvar) ' ∈ instfields(class0), r0 ≠ jvmref ∧ (r0 -- _type) × typeval(mkclasstype(class0)) ∈ st ∧ goodfieldsandtypes(r0, instfields(class0), st), r0 -- _type ∈ st, r0 ∈ st, validrefs(str, r1 ', ty0, st), is_obj(str, r0, st), class0 ≤ class1 ⊦ r0 = jvmref, is_reftype(ty0)

Rule argument

[speclemmaarg: , is_obj(r, class, st) ↔ r ≠ jvmref ∧ (r -- _type) × typeval(mkclasstype(class)) ∈ st ∧ goodfieldsandtypes(r, instfields(class), st) ,[st, class, r] → [st, class0, r0] ,F ,addfuns , ,is_obj-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, class0, r0)]]