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Proof step 57 from proof contains-subspec (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
tys ≠ [] ⊦ tys + tys0 = ty ' + tys1 ↔ ty = tys .first ∧ tys1 = tys .rest + tys0
Proof step 56:
tys ≠ [], ty3 = tys .first ∧ tys1 = tys .rest + ty0 ', has_classtype(ty), same-subclasses-contains(ty .jtelemtype .class, str, str0), level⊆(str0, str), type∃(str, ty), contains(str0, ty3 ' + tys1), type∃(str0, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str0, ty), ty0 ∈ tys1, ty3 ∈ tys, is_classtype(ty1) → ¬ interface∃(str0, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, str0, str, ty, tys0. # tys0 < # tys → ( has_classtype(ty) ∧ same-subclasses-contains(ty .jtelemtype .class, str, str0) ∧ level⊆(str0, str) ∧ type∃(str, ty) ∧ contains(str0, ty ' + tys0 + ty0 ') → contains(str, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys1 = [], contains(str, ty, ty0), dups(tys), ty ∈ tys

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