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Proof step 13 from proof contains-trans (previous step)

contains(str, ty0, ty1), contains(str, ty, ty0) ⊦ contains(str, ty, ty1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ contains(str, ty, ty0) ↔ (∃ tys. contains(str, ty ' + (tys + ty0)) ∧ ¬ dups(ty ' + tys))
Proof step 12:
∃ tys. contains(str, ty0 ' + (tys + ty1)) ∧ ¬ dups(ty0 ' + tys), contains(str, ty, ty0) ⊦ contains(str, ty, ty1)

Rule argument

[crewrite-arg: contains-type-def-nodups , F , [ty0, ty, str] → [ty1, ty0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty1, ty0, str)]]