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Proof step 56 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 = [], contains(str, ty, tys0 .last), tys0 .last ≤ ty ∧ type∃(str, tys0 .last)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ contains(str, ty, ty0) ↔ (∃ tys. contains(str, ty ' + (tys + ty0)))
Proof step 55:
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 = [], ∃ tys. contains(str, ty ' + (tys + tys0 .last)), tys0 .last ≤ ty ∧ type∃(str, tys0 .last)

Rule argument

[crewrite-arg: contains-type-def , F , [ty0, ty, str] → [tys0 .last, ty, str] ]

Additional information

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