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Proof step 24 from proof contains-levelsubset (previous step)

type∃(str0, ty1), type∃(str, ty0), level⊆(str, str0), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str, ty1), type∃(str0, ty), is_classtype(ty1), type∃(str0, ty0), type∃(str0, ty1), 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) ⊦ interface∃(str, ty1 .class), ∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, ty0), ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
type∃(str0, ty1), type∃(str, ty0), level⊆(str, str0), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str, ty1), type∃(str0, ty), is_classtype(ty1), type∃(str0, ty0), type∃(str0, ty1), 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) ⊦ interface∃(str, ty1 .class), ∃ ty1, ty2. ty1 ≤ ty ∧ type∃(str0, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ contains(str0, ty2, ty0), ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]