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Proof step 52 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), tys0 .last ≤ ty ∧ type∃(str, tys0 .last)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ tys ≠ [] → ( contains(str, ty ' + tys) ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ tys .first ≤ fs .type)) ∧ (is_arraytype(ty1) → tys .first ≤ ty1 .type) ∧ contains(str, tys)))
Proof step 51:
tys0 ≠ [], type∃(str, ty), ty0 ≤ ty, type∃(str, ty0) ∧ is_reftype(ty0) ∧ (∃ ty1. ty1 ≤ ty0 ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ tys0 .first ≤ fs .type)) ∧ (is_arraytype(ty1) → tys0 .first ≤ ty1 .type) ∧ contains(str, 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), tys0 .last ≤ ty ∧ type∃(str, tys0 .last)

Rule argument

[crewrite-arg: contains-rec-01, F, [tys, ty, str] → [tys0, ty0, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (tys0, ty0, str)]]