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Proof step 13 from proof contains-append (previous step)

tys1 + ty ' = ty2 ' + tys, contains(str, ty ' + tys0), contains(str, ty2 ' + tys), type∃(str, ty0), is_reftype(ty0), contains(str, tys1 + ty ' + tys0), type∃(str, ty1), ty1 ≤ ty0, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty3, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty2 ≤ ty3, is_arraytype(ty1) → ty2 ≤ ty1 .type ⊦ ty ≠ ty2 ∧ ¬ ty ∈ tys, ¬ ty2 ∈ tys1 ∧ ty2 ≠ ty, ty1 ≤ ty0 ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
tys1 + ty ' = ty2 ' + tys, contains(str, ty ' + tys0), contains(str, ty2 ' + tys), type∃(str, ty0), is_reftype(ty0), contains(str, tys1 + ty ' + tys0), type∃(str, ty1), ty1 ≤ ty0, is_classtype(ty1), mkfs(class, ty3, fieldvar) ' ∈ instfields(ty1 .class), ty2 ≤ ty3 ⊦ interface∃(str, ty1 .class), ty ≠ ty2 ∧ ¬ ty ∈ tys, ¬ ty2 ∈ tys1 ∧ ty2 ≠ ty, ∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_classtype(ty) → ¬ is_arraytype(ty)])]]