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Proof step 25 from proof contains-trans-01 (previous step)

contains(str, ty ' + tys + ty0 '), contains(str, ty0 ' + tys0 + ty1 '), ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ contains(str, ty ' + tys + ty0 ' + tys0 + ty1 ')

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 24:
tys + ty0 ' + tys0 + ty1 ' ≠ [], contains(str, ty ' + tys + ty0 '), contains(str, ty0 ' + tys0 + ty1 '), ∀ ty, ty1, tys0, ty0, str, tys1. # tys1 < # tys → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty2. ty2 ≤ ty ∧ type∃(str, ty2) ∧ (is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ (∃ fs. fs ' ∈ instfields(ty2 .class) ∧ (tys + ty0 ' + tys0 + ty1 ') .first ≤ fs .type)) ∧ (is_arraytype(ty2) → (tys + ty0 ' + tys0 + ty1 ') .first ≤ ty2 .type) ∧ contains(str, tys + ty0 ' + tys0 + ty1 '))

Rule argument

[crewrite-arg: contains-rec-01 , F , [tys, ty, str] → [tys + ty0 ' + tys0 + ty1 ', ty, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ tys + tys0 ≠ [] ↔ tys = [] ∧ tys0 = []], [CSIMPSEQ : ⊦ ty ' ≠ []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])], [EXTRATERMS : (tys + ty0 ' + tys0 + ty1 ', ty, str)]]