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Proof step 9 from proof contains-trans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ contains(str, ty, ty0) ↔ (∃ tys. contains(str, ty ' + (tys + ty0)))
Proof step 8:
contains(str, ty0 ' + tys + ty1 '), contains(str, ty ' + tys0 + ty0 ') ⊦ ∃ tys. contains(str, ty ' + (tys + ty1)), dups(tys), ty0 ∈ tys, dups(tys0), ty ∈ tys0

Rule argument

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

Additional information

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