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Proof step 66 from proof contains-levelsubset (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 32:
tys1 = [], tys + ty0 ' = ty3 ' + tys1, level⊆(str, str0), contains(str, ty3 ' + tys1), type∃(str, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ contains(str0, ty, ty0), dups(tys), ty ∈ tys, ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys1, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0
Proof step 65:
tys + ty0 ' = ty3 ' + tys1, level⊆(str, str0), contains(str, ty3 ' + tys1), type∃(str, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys1 = [], contains(str0, ty, ty0), dups(tys), ty ∈ tys, ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys1, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0

Rule argument

[fma-arg: tys1 = []]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (tys1 = [])]]