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Proof step 33 from proof validrefs-subset (previous step)

st0[r0 -- mkfs(class, ty1, fieldvar) '] = refval(r), validrefs(str, r ' + refs, ty1, st0), mkfs(class, ty1, fieldvar) ' ∈ instfields(st0[r0 -- _type] .type .class), st0[r0 -- _type] .type ≤ ty, is_valid_ref(str, r0, st0), st ⊆ st0, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str0, ty0, st1, st2. validrefs(str0, r ' + refs, ty0, st1) ∧ st2 ⊆ st1 ∧ ¬ junkref(str0, r, st2) → validrefs(str0, r ' + refs, ty0, st2) ⊦ r0 = jvmref, junkref(str, r0, st), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- mkfs(class, ty1, fieldvar) ']) ∧ r = st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ∧ validrefs(str, st[r0 -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,st1 ⊆ st2 ↔ (∀ rk. rk ∈ st1 → rk ∈ st2 ∧ st1[rk] = st2[rk]) ,[st2, st1] → [st0, st] ,F ,store ,javastore-ostorea ,Subset ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st0, st)]]