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Proof step 74 from proof contains-levelsubset (previous step)

level⊆(str, str0), contains(str, ty ' + tys + ty0 ') ⊦ contains(str0, ty, ty0), dups(tys), ty ∈ tys

User applied rule induction

And obtained the following new goals

Proof step 73:
level⊆(str, str0) ∧ contains(str, ty ' + tys + ty0 '), ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ contains(str0, ty, ty0) ∨ dups(tys) ∨ ty ∈ tys

Rule argument

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

Additional information

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