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Proof step 11 from proof contains-trans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ contains(str, ty, ty0) ↔ (∃ tys. contains(str, ty ' + (tys + ty0)) ∧ ¬ dups(ty ' + tys))
Proof step 10:
∃ tys. contains(str, ty ' + (tys + ty0)) ∧ ¬ dups(ty ' + tys), contains(str, ty0 ' + tys + ty1 ') ⊦ contains(str, ty, ty1), dups(tys), ty0 ∈ tys

Rule argument

[crewrite-arg: contains-type-def-nodups , F , [ty0, ty, str] → [ty0, ty, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty0, ty, str)]]