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Proof step 32 from proof contains-levelsubset (previous step)

tys1 = [], tys + ty0 ' = ty3 ' + tys1, level⊆(str, str0), contains(str, ty3 ' + tys1), type∃(str, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), 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) ⊦ contains(str0, ty, ty0), dups(tys), ty ∈ tys, ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys1, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ contains(str, ty ') ↔ type∃(str, ty)
Proof step 31:
type∃(str, ty0), level⊆(str, str0), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str, ty1), is_arraytype(ty1) → ty0 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty0 ≤ ty2, ∀ ty0, ty, str0, str, tys0. # tys0 < # [] → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ contains(str0, ty, ty0)

Rule argument

[emptyarg]

Additional information

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