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Proof step 23 from proof contains-trans-01 (previous step)

contains(str, ty ' + tys + ty0 '), contains(str, ty0 ' + tys0 + ty1 '), ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty2. ty2 ≤ ty ∧ type∃(str, ty2) ∧ (is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ (∃ fs. fs ' ∈ instfields(ty2 .class) ∧ (tys + ty0 ') .first ≤ fs .type)) ∧ (is_arraytype(ty2) → (tys + ty0 ') .first ≤ ty2 .type) ∧ contains(str, tys + ty0 ' + tys0 + ty1 '))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
tys + ty0 ' = ty3 + tys2 ∧ tys + ty0 ' ≠ [], contains(str, ty ' + tys + ty0 '), contains(str, ty0 ' + tys0 + ty1 '), ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty2. ty2 ≤ ty ∧ type∃(str, ty2) ∧ (is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ (∃ fs. fs ' ∈ instfields(ty2 .class) ∧ ty3 ≤ fs .type)) ∧ (is_arraytype(ty2) → ty3 ≤ ty2 .type) ∧ contains(str, tys + ty0 ' + tys0 + ty1 '))

Rule argument

[speclemmaarg: tys ≠ [] ,ty = tys .first ∧ tys0 = tys .rest ↔ tys = ty + tys0 ,[tys, ty, tys0] → [tys + ty0 ', ty3, tys2] ,T ,list-data ,javatypes ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ tys + tys0 ≠ [] ↔ tys = [] ∧ tys0 = []], [CSIMPSEQ : ⊦ ty ' ≠ []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPELIM : tys ≠ [] ⊦ ty = tys .first ∧ tys0 = tys .rest ↔ tys = ty + tys0])], [EXTRATERMS : (tys + ty0 ', ty3, tys2)]]