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Proof step 5 from proof contains-trans (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 4:
⊦ contains(str, ty ' + tys + ty0 ') ∧ contains(str, ty0 ' + tys0 + ty1 ') → contains(str, ty ' + tys + ty0 ' + tys0 + ty1 ')

Rule argument

[LEMMAARG : contains-trans-01, [str, ty, tys, ty0, tys0, ty1] → [str, ty, tys0, ty0, tys, ty1]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])], [EXTRATERMS : (str, ty, tys0, ty0, tys, ty1)]]