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Proof step 14 from proof exvalidrefs (previous step)

st[r -- _type] = typeval(mkclasstype(st[r -- _type] .type .class)), r -- _type ∈ st, is_typevalue(st[r -- _type]), is_classtype(st[r -- _type] .type), is_obj(r, st[r -- _type] .type .class, st), class+∃(str, st[r -- _type] .type .class), mkfs(class, st[r -- _type] .type, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), r ∈ st, ∀ ty. type∃(str, ty) → (ty ≤ st[r -- _type] .type → ty = st[r -- _type] .type), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∀ ty. type∃(str, ty) → (ty ≤ st0[r -- _type] .type ↔ ty = st0[r -- _type] .type)) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ fs .type = st0[r -- _type] .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, is_abstract(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, st[r -- _type] .type, fieldvar) ']), cyclic(str, r, st), ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st[r -- fs ']) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
st[r -- _type] .type = mkclasstype(class0), st[r -- _type] = typeval(mkclasstype(class0)), r -- _type ∈ st, is_typevalue(st[r -- _type]), is_classtype(st[r -- _type] .type), is_obj(r, class0, st), class+∃(str, class0), mkfs(class, st[r -- _type] .type, fieldvar) ' ∈ instfields(class0), r ∈ st, ∀ ty. type∃(str, ty) → (ty ≤ st[r -- _type] .type → ty = st[r -- _type] .type), ∀ r, str, st0. # st0 .refs < # st .refs → ( ¬ junkref(str, r, st0) ∧ ¬ cyclic(str, r, st0) ∧ is_obj(str, r, st0) ∧ r ≠ jvmref ∧ (∀ ty. type∃(str, ty) → (ty ≤ st0[r -- _type] .type ↔ ty = st0[r -- _type] .type)) ∧ (∃ fs. fs ' ∈ instfields(st0[r -- _type] .type .class) ∧ fs .type = st0[r -- _type] .type) → (∃ refs. validrefs(str, refs, st0[r -- _type] .type, st0) ∧ refs ≠ [] ∧ refs .first = r ∧ refs .last = jvmref)) ⊦ r = jvmref, is_abstract(class0), is_referencevalue(st[r -- mkfs(class, st[r -- _type] .type, fieldvar) ']), cyclic(str, r, st), ∃ fs. fs ' ∈ instfields(class0) ∧ (is_reftype(fs .type) ∨ fs .type = abstract_type) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_referencevalue(st[r -- fs ']) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ junkref(str, st[r -- fs '] .refval, st))

Rule argument

[speclemmaarg: ,is_classtype(ty) → (class = ty .class ↔ ty = mkclasstype(class)) ,[ty, class] → [st[r -- _type] .type, class0] ,T ,javatype , ,elim-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_classtype(ty) → ( class = ty .class ↔ ty = mkclasstype(class))])], [EXTRATERMS : (st[r -- _type] .type, class0)]]