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Proof step 65 from proof contains-subspec (previous step)

contains(str0, ty ' + tys + ty0 '), type∃(str, ty), level⊆(str0, str), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ level⊆(str0, str) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ ty ∈ tys, dups(tys), contains(str, ty, ty0)

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 64:
tys + ty0 ' ≠ [], type∃(str0, ty) ∧ is_reftype(ty) ∧ (∃ ty1. ty1 ≤ ty ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ (tys + ty0 ') .first ≤ fs .type)) ∧ (is_arraytype(ty1) → (tys + ty0 ') .first ≤ ty1 .type) ∧ contains(str0, tys + ty0 ')), type∃(str, ty), level⊆(str0, str), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ level⊆(str0, str) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ ty ∈ tys, dups(tys), contains(str, ty, ty0)

Rule argument

[crewrite-arg: contains-rec-01 , F , [tys, ty, str] → [tys + ty0 ', ty, str0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ tys + tys0 ≠ [] ↔ tys = [] ∧ tys0 = []], [CSIMPSEQ : ⊦ ty ' ≠ []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])], [EXTRATERMS : (tys + ty0 ', ty, str0)]]