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Proof step 42 from proof contains-subspec (previous step)

type∃(str, ty1), contains(str0, (ty3 ' + tys1) + ty0 '), type∃(str, ty), level⊆(str0, str), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), type∃(str0, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, str0, str, ty, tys0. # tys0 < # (ty3 + tys1) → ( 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 = ty3, has_classtype(ty3), ty ∈ tys1, ty3 ∈ tys1, dups(tys1), contains(str, ty3, ty0), ∃ tys. contains(str0, ty3 ' + (tys + ty0)), ∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ type∃(str, ty0) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 41:
type∃(str, ty1), contains(str0, (ty3 ' + tys1) + ty0 '), type∃(str, ty), level⊆(str0, str), same-subclasses-contains(ty .jtelemtype .class, str, str0), has_classtype(ty), type∃(str0, ty), is_reftype(ty), ty1 ≤ ty, type∃(str0, ty1), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, str0, str, ty, tys0. # tys0 < # (ty3 + tys1) → ( 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 = ty3, has_classtype(ty3), ty ∈ tys1, ty3 ∈ tys1, dups(tys1), contains(str, ty3, ty0), ∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ type∃(str, ty0) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type), ∃ tys. contains(str0, ty3 ' + tys + ty0 ')

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ tys + ty = tys + ty '])]]