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

tdname+∃(str0, class1), contains(str0, ty3, ty4), level⊆(str, str0), contains(str, ty3 ' + tys2 + ty4 '), class0 ≤ class1, tdname+∃(str, class1), ty3 ≤ ty2, mkfs(class, ty2, fieldvar) ' ∈ instfields(class0), tdname+∃(str0, class0), interface∃(str0, class0), class∃(str, class0), ∀ ty0, ty, str0, str, tys0. # tys0 < # (ty3 ' + tys2) → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ mkclasstype(class1) = ty3, ty3 ∈ tys2, dups(tys2), mkclasstype(class1) ∈ tys2, ∃ ty1. ty1 ≤ mkclasstype(class1) ∧ type∃(str0, ty1) ∧ type∃(str0, ty4) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty4 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty4 ≤ ty1 .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ level⊆(str, str0) ↔ (∀ class. class∃(str, class) → class∃(str0, class)) ∧ (∀ class. interface∃(str, class) → interface∃(str0, class))
Proof step 41:
tdname+∃(str0, class1), contains(str0, ty3, ty4), (∀ class. class∃(str, class) → class∃(str0, class)) ∧ (∀ class. interface∃(str, class) → interface∃(str0, class)), contains(str, ty3 ' + tys2 + ty4 '), class0 ≤ class1, tdname+∃(str, class1), ty3 ≤ ty2, mkfs(class, ty2, fieldvar) ' ∈ instfields(class0), tdname+∃(str0, class0), interface∃(str0, class0), class∃(str, class0), ∀ ty0, ty, str0, str, tys0. # tys0 < # (ty3 ' + tys2) → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ mkclasstype(class1) = ty3, ty3 ∈ tys2, dups(tys2), mkclasstype(class1) ∈ tys2, ∃ ty1. ty1 ≤ mkclasstype(class1) ∧ type∃(str0, ty1) ∧ type∃(str0, ty4) ∧ (is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty4 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty4 ≤ ty1 .type)

Rule argument

[speclemmaarg: , level⊆(str, str0) ↔ (∀ class. class∃(str, class) → class∃(str0, class)) ∧ (∀ class. interface∃(str, class) → interface∃(str0, class)) ,[str0, str] → [str0, str] ,F ,junkrefs , ,levelsubset-def ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (str0, str)]]