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Proof step 23 from proof validrefs-subset (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , is_obj(str, r, st) → ( junkref(str, r, st) ↔ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ ( ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st)))) ,[st, r, str] → [st, r0, str] ,F ,junkrefs , ,junkref-class ]

Additional information

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