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Proof step 6 from proof contains-bytearray (conclusion)

⊦ contains(str, mkarraytype(byte_type) ' + tys + ty ') ↔ tys = [] ∧ ty = byte_type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 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 5:
tys + ty ' ≠ [] ⊦ type∃(str, mkarraytype(byte_type)) ∧ is_reftype(mkarraytype(byte_type)) ∧ (∃ ty1. ty1 ≤ mkarraytype(byte_type) ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ (tys + ty ') .first ≤ fs .type)) ∧ (is_arraytype(ty1) → (tys + ty ') .first ≤ ty1 .type) ∧ contains(str, tys + ty ')) ↔ tys = [] ∧ ty = byte_type

Rule argument

[crewrite-arg: contains-rec-01 , F , [tys, ty, str] → [tys + ty ', mkarraytype(byte_type), str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ tys + tys0 ≠ [] ↔ tys = [] ∧ tys0 = []], [CSIMPSEQ : ⊦ ty ' ≠ []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])], [EXTRATERMS : (tys + ty ', mkarraytype(byte_type), str)]]