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Proof step 24 from proof validrefs-subset-equiv (previous step)

st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), r -- mkfs(class, ty0, fieldvar) ' ∈ st, r -- _type ∈ st, validrefs(str, r0 ' + refs1, ty0, st0), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), st ⊆ st0, st[r -- _type] .type ≤ ty, is_obj(str, r, st), r ∈ st, junkref(str, r0, st), ∀ st, st1, ty, r1, str, refs0. # refs0 < # (r0 + refs1) → (validrefs(str, r1 ' + refs0, ty, st1) ∧ st ⊆ st1 ∧ validref(str, r1, st[r1 -- _type] .type, st) → validrefs(str, r1 ' + refs0, ty, st)) ⊦ r = jvmref, validrefs(str, r0 ' + refs1, ty0, st), junkref(str, r, 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, r, str] ,F ,junkrefs , ,junkref-class ]

Additional information

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