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Proof step 64 from proof validref-subspec-samesubclasses (previous step)

tdname+∃(str0, class), same-subclasses-contains(class, str, str0), okreftype(refval(r), mkclasstype(class), st), junkref(str, r, st) ⊦ junkref(str0, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 63:
tdname+∃(str0, class), same-subclasses-contains(class, str, str0), is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st ∧ is_typevalue(st[refval(r) .refval -- _type]) ∧ st[refval(r) .refval -- _type] .type ≤ mkclasstype(class)), junkref(str, r, st) ⊦ junkref(str0, r, st), same-subclasses-contains(st[r -- _type] .type .jtelemtype .class, str, str0)

Rule argument

[speclemmaarg: , okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ ( val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty) ,[st, ty, val] → [st, mkclasstype(class), refval(r)] ,F ,okfuns , ,okreftype ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mkclasstype(class), refval(r))]]