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Proof step 65 from proof contains-field-def-case (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 64:
⊦ contains(str, ty ') ↔ type∃(str, ty)

Rule argument

[EXRARG : pos: right 1, [extquanttermlist: (ty0 ')abort:F, discard:T, computed:F]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ' ≠ []], [CSIMPSEQ : ⊦ ty ' .first = ty], [CSIMPSEQ : ⊦ ty ' .last = ty])], [EXTRATERMS : (ty0 ')]]