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Proof step 4 from proof contains-append (previous step)

contains(str, ty ' + tys0) ⊦ type∃(str, ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ tys ≠ [] → ( contains(str, ty ' + tys) ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ tys .first ≤ fs .type)) ∧ (is_arraytype(ty1) → tys .first ≤ ty1 .type) ∧ contains(str, tys)))
Proof step 3:
⊦ contains(str, ty ') ↔ type∃(str, ty)

Rule argument

[crewrite-arg: contains-rec-01, F, [tys, ty, str] → [tys0, ty, str]]

Additional information

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