[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 67 from proof contains-subspec (previous step)

has_classtype(ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), level⊆(str0, str), type∃(str, ty), contains(str0, ty ' + tys + ty0 ') ⊦ contains(str, ty, ty0), dups(tys), ty ∈ tys

User applied rule induction

And obtained the following new goals

Proof step 66:
has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ level⊆(str0, str) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys + ty0 '), ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ level⊆(str0, str) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ contains(str, ty, ty0) ∨ dups(tys) ∨ ty ∈ tys

Rule argument

[INDHYPARG : [STANDARDINDUCTIONTYPE : ], true, false, # tys, [] → [], <]

Additional information

[[CONCRETESIMPRULES : ([CSIMPLESSPRED : <])], [EXTRATERMS : (# tys)]]