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Proof step 63 from proof contains-levelsubset (previous step)

contains(str0, ty3, tys1 .last) ∨ dups(tys1 .butlast) ∨ ty3 ∈ tys1 .butlast, tys + ty0 ' = ty3 ' + tys1, level⊆(str, str0), contains(str, ty3 ' + tys1), type∃(str, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), ty0 ∈ tys1, ty3 ∈ tys, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys1 = [], contains(str0, ty, ty0), dups(tys), ty ∈ tys

User applied rule insert elim lemma

And obtained the following new goals

Proof step 62:
tys1 = tys2 + ty4 ', contains(str0, ty3, ty4) ∨ dups(tys2) ∨ ty3 ∈ tys2, tys + ty0 ' = ty3 ' + tys1, level⊆(str, str0), contains(str, ty3 ' + tys1), type∃(str, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), ty0 ∈ tys1, ty3 ∈ tys, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys1 = [], contains(str0, ty, ty0), dups(tys), ty ∈ tys

Rule argument

[speclemmaarg: tys ≠ [] ,ty = tys .last ∧ tys0 = tys .butlast ↔ tys = tys0 + ty ' ,[tys, ty, tys0] → [tys1, ty4, tys2] ,T ,list-last ,javatypes ,last-elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : tys ≠ [] ⊦ ty = tys .last ∧ tys0 = tys .butlast ↔ tys = tys0 + ty '])], [EXTRATERMS : (tys1, ty4, tys2)]]