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Proof step 3 from proof contains-bytearray-04 (previous step)

contains(str, mkarraytype(byte_type), ty) ⊦ ty = byte_type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ contains(str, ty, ty0) ↔ type∃(str, ty) ∧ is_reftype(ty) ∧ ( (∃ ty1. ty1 ≤ ty ∧ type∃(str, ty1) ∧ type∃(str, ty0) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type)) ∨ (∃ ty1, ty2. 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) ∧ contains(str, ty2, ty0)))
Proof step 2:
⊦ ¬ contains(str, byte_type, ty)

Rule argument

[crewrite-arg: contains-type-rec , F , [ty0, ty, str] → [ty, mkarraytype(byte_type), str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ type∃(str, mkarraytype(ty)) ↔ type∃(str, ty)], [CSIMPSEQ : ⊦ type∃(str, byte_type)], [CSIMPSEQ : ⊦ is_reftype(mkarraytype(ty))], [CSIMPSEQ : ⊦ ty ≤ mkarraytype(byte_type) ↔ ty = mkarraytype(byte_type)], [CSIMPSEQ : ⊦ ¬ is_classtype(mkarraytype(ty))], [CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [CSIMPSEQ : ⊦ ty ≤ byte_type ↔ ty = byte_type])], [EXTRATERMS : (ty, mkarraytype(byte_type), str)]]