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Proof step 14 from proof contains-trans-01 (previous step)

tys + ty0 ' = ty3 ' + tys2, contains(str, ty0 ' + tys0 + ty1 '), type∃(str, ty), is_reftype(ty), ty2 ≤ ty, type∃(str, ty2), contains(str, ty3 ' + tys2), is_arraytype(ty2) → ty3 ≤ ty2 .type, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ mkfs(class, ty4, fieldvar) ' ∈ instfields(ty2 .class) ∧ ty3 ≤ ty4, ∀ 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, tys + ty0 ' + tys0 + ty1 '), ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys2, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
tys ≠ [] ⊦ tys + tys0 = ty ' + tys1 ↔ ty = tys .first ∧ tys1 = tys .rest + tys0
Proof step 13:
tys ≠ [], ty3 = tys .first ∧ tys2 = tys .rest + ty0 ', contains(str, ty0 ' + tys0 + ty1 '), type∃(str, ty), is_reftype(ty), ty2 ≤ ty, type∃(str, ty2), contains(str, ty3 ' + tys2), is_arraytype(ty2) → ty3 ≤ ty2 .type, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ mkfs(class, ty4, fieldvar) ' ∈ instfields(ty2 .class) ∧ ty3 ≤ ty4, ∀ 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, tys + ty0 ' + tys0 + ty1 '), ty0 ≠ ty3 ∧ ¬ ty0 ∈ tys2, ¬ ty3 ∈ tys ∧ ty3 ≠ ty0

Rule argument

[speclemmaarg: tys ≠ [] ,tys + tys0 = ty ' + tys1 ↔ ty = tys .first ∧ tys1 = tys .rest + tys0 ,[tys1, ty, tys0, tys] → [tys2, ty3, ty0 ', tys] ,F ,list ,javatypes ,firsteq-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ [] + tys = tys], [CSIMPSEQ : ⊦ ty ' = ty0 ' + tys ↔ ty = ty0 ∧ tys = []])], [EXTRATERMS : (tys2, ty3, ty0 ', tys)]]