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Proof step 55 from proof contains-levelsubset (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 54:
type∃(str0, ty1), type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str, ty1), contains(str, ty3 ' + tys2 + ty4 '), level⊆(str, str0), contains(str0, ty3, ty4), type∃(str0, ty), is_classtype(ty1), type∃(str0, ty1), mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class), ty3 ≤ ty2, ∀ ty0, ty, str0, str, tys0. # tys0 < # (ty3 ' + tys2) → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ ty = ty3, ty ∈ tys2, dups(tys2), ty3 ∈ tys2, interface∃(str, ty1 .class), ∃ ty1. ty1 ≤ ty ∧ 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), ¬ interface∃(str0, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty3 ≤ fs .type)

Rule argument

[fma-arg: type∃(str0, ty1)]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRAFMAS : (type∃(str0, ty1))]]