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Proof step 37 from proof same-subclasses-class-forward (previous step)

st[r -- mkfs(class, ty, fieldvar) '] = refval(r0), is_obj(str0, r, st), has_classtype(st[r0 -- _type] .type), mkfs(class, ty, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), same-subclasses(st[r -- _type] .type .class, str, str0), is_obj(str, r, st), is_obj(r, st), st[r0 -- _type] .type ≤ ty, is_valid_ref(str0, r0, st), type∃(str0, st[r -- _type] .type), ∀ class0. contains(str0, mkclasstype(st[r -- _type] .type .class), mkclasstype(class0)) → same-subclasses(class0, str, str0) ⊦ r = jvmref, r0 = jvmref, tdname+∃(str0, st[r -- _type] .type .class), contains(str0, mkclasstype(st[r -- _type] .type .class), st[r0 -- _type] .type .jtelemtype), junkref(str0, r0, st), same-subclasses(st[r0 -- _type] .type .jtelemtype .class, str, str0) ∧ (contains(str0, st[r0 -- _type] .type .jtelemtype, mkclasstype(class0)) → same-subclasses(class0, str, str0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ type∃(str, ty) ↔ ¬ has_classtype(ty) ∨ tdname+∃(str, ty .jtclass)

Rule argument

[speclemmaarg: ,type∃(str, ty) ↔ ¬ has_classtype(ty) ∨ tdname+∃(str, ty .jtclass) ,[ty, str] → [st[r -- _type] .type, str0] ,F ,typefuns , ,typeex-def ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty .jtclass = ty .jtelemtype .class], [CSIMPSEQ : ⊦ is_obj(r, st) → st[r -- _type] .type .jtelemtype = st[r -- _type] .type], [CSIMPSEQ : ⊦ ¬ has_classtype (st[r -- _type] .type) → ¬ is_obj(str, r, st)])], [EXTRATERMS : (st[r -- _type] .type, str0)]]