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Proof step 34 from proof contains-levelsubset (previous step)

tys + ty0 ' = ty3 ' + tys1, # tys < # tys1, ty3 ∈ tys, ty0 ∈ tys1, type∃(str, ty), is_reftype(ty), ty1 ≤ ty, type∃(str, ty1), contains(str, ty3 ' + tys1), level⊆(str, str0), is_arraytype(ty1) → ty3 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys1 = [], ty ∈ tys, dups(tys), contains(str0, ty, ty0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: tys ≠ [] ,tys + tys0 = ty ' + tys1 ↔ ty = tys .first ∧ tys1 = tys .rest + tys0 ,[tys1, ty, tys0, tys] → [tys1, ty3, ty0 ', tys] ,F ,list ,javatypes ,firsteq-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ' = ty0 ' + tys ↔ ty = ty0 ∧ tys = []], [CSIMPSEQ : ⊦ [] + tys = tys], [CSIMPSEQ : ⊦ tys + ty ' ≠ []], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ # (tys + tys0) = # tys + # tys0], [CSIMPSEQ : ⊦ tys ≠ [] → # tys .rest = (# tys) -1], [CSIMPSEQ : ⊦ n -1 = n - 1], [CSIMPSEQ : ⊦ # ty ' = 0 +1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ # tys = 0 ↔ tys = []], [CSIMPSEQ : ⊦ m < 1 ↔ m = 0], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : n0 ≤ n ⊦ n - n0 < m ↔ n < m + n0], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (tys1, ty3, ty0 ', tys)]]