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Proof step 70 from proof contains-field-def-case (previous step)

contains(str, ty, ty0), type∃(str, ty), is_reftype(ty0), is_classtype(ty0) → ¬ interface∃(str, ty0 .class) ∧ fs ' ∈ instfields(ty0 .class), is_arraytype(ty0) → fs ' = _length ⊦ ∃ 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 insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ contains(str, ty, ty0) ↔ (∃ tys. contains(str, ty ' + (tys + ty0)))
Proof step 69:
∃ tys. contains(str, ty ' + (tys + ty0)), type∃(str, ty), is_reftype(ty0), is_classtype(ty0) → ¬ interface∃(str, ty0 .class) ∧ fs ' ∈ instfields(ty0 .class), is_arraytype(ty0) → fs ' = _length ⊦ ∃ 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)

Rule argument

[crewrite-arg: contains-type-def, F, [ty0, ty, str] → [ty0, ty, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty0, ty, str)]]