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Proof step 25 from proof contains-field-def-case (previous step)

ty1 ≤ ty, type∃(str, ty), ty0 ≤ ty, type∃(str, ty0), is_reftype(ty0), ty1 ≤ ty0, type∃(str, ty1), type∃(str, ty2), is_reftype(ty2), is_arraytype(ty1) → ty2 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty3, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty2 ≤ ty3, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ fs ' ∈ instfields(ty2 .class), is_arraytype(ty2) → fs ' = _length ⊦ contains(str, ty ' + ty2 '), ty2 ≤ ty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ contains(str, ty ' + ty0 ') ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type) ∧ type∃(str, ty0))
Proof step 24:
ty1 ≤ ty, type∃(str, ty), ty0 ≤ ty, type∃(str, ty0), is_reftype(ty0), ty1 ≤ ty0, type∃(str, ty1), type∃(str, ty2), is_reftype(ty2), is_arraytype(ty1) → ty2 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty3, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty2 ≤ ty3, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ fs ' ∈ instfields(ty2 .class), is_arraytype(ty2) → fs ' = _length ⊦ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty2 ≤ ty1 .type) ∧ type∃(str, ty2)), ty2 ≤ ty

Rule argument

[crewrite-arg: contains-two, F, [ty0, ty, str] → [ty2, ty, str]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (ty2, ty, str)]]