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Proof step 58 from proof contains-field-def-case (previous step)

type∃(str, ty), ty0 ≤ ty, contains(str, ty0 ' + tys0), is_reftype(tys0 .last), is_classtype(tys0 .last) → ¬ interface∃(str, tys0 .last .class) ∧ fs ' ∈ instfields(tys0 .last .class), is_arraytype(tys0 .last) → fs ' = _length ⊦ tys0 = [], ∃ ty1. (ty1 ≤ ty ∧ type∃(str, ty1) ∨ contains(str, ty, ty1)) ∧ is_reftype(ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ fs ' ∈ instfields(ty1 .class)) ∧ (is_arraytype(ty1) → fs ' = _length)

User applied rule exists right

And obtained the following new goals

Proof step 57:
type∃(str, ty), ty0 ≤ ty, contains(str, ty0 ' + tys0), is_reftype(tys0 .last), is_classtype(tys0 .last) → ¬ interface∃(str, tys0 .last .class) ∧ fs ' ∈ instfields(tys0 .last .class), is_arraytype(tys0 .last) → fs ' = _length ⊦ tys0 = [], (tys0 .last ≤ ty ∧ type∃(str, tys0 .last) ∨ contains(str, ty, tys0 .last)) ∧ is_reftype(tys0 .last) ∧ (is_classtype(tys0 .last) → ¬ interface∃(str, tys0 .last .class) ∧ fs ' ∈ instfields(tys0 .last .class)) ∧ (is_arraytype(tys0 .last) → fs ' = _length)

Rule argument

[EXRARG : pos: right 2, [extquanttermlist: (tys0 .last) abort:F , discard:T , computed:T ]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (tys0 .last)]]