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Proof step 6 from proof contains-trans-01 (previous step)

ty2 = mkclasstype(class0), tys + ty0 ' = ty3 ' + tys2, is_classtype(ty2), contains(str, ty0 ' + tys0 + ty1 '), type∃(str, ty), is_reftype(ty), ty2 ≤ ty, type∃(str, ty2), contains(str, ty3 ' + tys2), mkfs(class, ty4, fieldvar) ' ∈ instfields(class0), ty3 ≤ ty4, ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ interface∃(str, class0), ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys2, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0, ∃ fs. fs ' ∈ instfields(class0) ∧ ty3 ≤ fs .type

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
tys + ty0 ' = ty3 ' + tys2, contains(str, ty3 ' + tys2), mkfs(class, ty4, fieldvar) ' ∈ instfields(class0), ty3 ≤ ty4, contains(str, ty0 ' + tys0 + ty1 '), type∃(str, ty), is_classtype(ty), class0 ≤ ty .class, tdname+∃(str, class0), ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ interface∃(str, class0), ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys2, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0, ∃ fs. fs ' ∈ instfields(class0) ∧ ty3 ≤ fs .type

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_classtype(ty) → is_reftype(ty)], [CSIMPSEQ : ⊦ type∃(str, mkclasstype(class)) ↔ tdname+∃(str, class)], [CSIMPSEQ : ⊦ mkclasstype(class) ≤ ty ↔ is_classtype(ty) ∧ class ≤ ty .class], [CSIMPSEQ : ⊦ is_classtype(mkclasstype(class))])]]