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Proof step 4 from proof compatarray-void (previous step)

st[r -- i '] = refval(r0), st[r -- _type] .type = mkarraytype(void_type), st[r -- _length] = intval(i0), st[r0 -- _type] = typeval(ty), 0 < i0, 0 ≤ i0, i < i0, r -- _length ∈ st, is_arrayref(r, i0, st), 0 ≤ i, r ∈ st, r0 -- _type ∈ st, is_reftype(ty), is_subtype(str, ty, void_type), r0 ∈ st, has_classtype(ty) → tdname+∃(str, ty .jtelemtype .class), is_classtype(ty) → class+∃(str, ty .class) ⊦ r0 = jvmref, r = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_subtype(str, ty1, ty2) ↔ ty1 ≤ ty2 ∧ (has_classtype(ty1) → tdname+∃(str, ty1 .jtclass)) ∧ (has_classtype(ty2) → tdname+∃(str, ty2 .jtclass))

Rule argument

[speclemmaarg: , is_subtype(str, ty1, ty2) ↔ ty1 ≤ ty2 ∧ (has_classtype(ty1) → tdname+∃(str, ty1 .jtclass)) ∧ (has_classtype(ty2) → tdname+∃(str, ty2 .jtclass)) ,[ty2, ty1, str] → [void_type, ty, str] ,F ,typefuns , ,is_subtype-level ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ void_type ↔ ty = void_type], [CSIMPSEQ : ⊦ ty .jtclass = ty .jtelemtype .class], [CSIMPSEQ : ⊦ ¬ has_classtype(void_type)], [CSIMPSEQ : ⊦ ¬ is_reftype(void_type)])], [EXTRATERMS : (void_type, ty, str)]]