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Proof step 5 from proof compatval-addclass (previous step)

st[r -- _type] = typeval(ty0), fis .keys = statfields(class), okfieldinits(class, fis), okval(refval(r), ty), r ≠ jvmref → r -- _type ∈ st ∧ is_reftype(ty0) ∧ (has_classtype(ty0) → tdname+∃(str, ty0 .jtelemtype .class)) ∧ (is_classtype(ty0) → class+∃(str, ty0 .class)) ∧ is_subtype(str, ty0, ty) ⊦ (ty = void_type ∨ is_reftype(ty)) ∧ ( r ≠ jvmref → r -- _type ∈ addclass(class, fis, st) ∧ is_reftype(ty0) ∧ ( has_classtype(ty0) → class∃(str, ty0 .jtelemtype .class) ∨ interface∃(str, ty0 .jtelemtype .class) ∨ is_predefined_class(ty0 .jtelemtype .class)) ∧ (is_classtype(ty0) → class+∃(str, ty0 .class)) ∧ is_subtype(str, ty0, ty))

User applied rule case distinction

And closed the goal!

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ okval(refval(r), ty) ↔ ty = void_type ∨ is_reftype(ty)], [CSIMPSEQ : ⊦ rk ∈ st → rk ∈ addclass(class, fis, st)], [CSIMPSEQ : ⊦ tdname+∃(str, class) ↔ tdname∃(str, class) ∨ is_predefined_class(class)], [CSIMPSEQ : ⊦ tdname∃(str, class) ↔ class∃(str, class) ∨ interface∃(str, class)])]]