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Proof step 27 from proof contains-trans-01 (previous step)

contains(str, ty0 ' + tys0 + ty1 '), contains(str, ty ' + tys + ty0 ') ⊦ contains(str, ty ' + tys + ty0 ' + tys0 + ty1 ')

User applied rule induction

And obtained the following new goals

Proof step 26:
contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys + ty0 '), ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ contains(str, ty ' + tys + ty0 ' + tys0 + ty1 ')

Rule argument

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

Additional information

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