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Proof step 64 from proof contains-levelsubset (previous step)

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

User applied rule apply induction

And obtained the following new goals

Proof step 35:
tys + ty0 ' = ty3 ' + tys1, level⊆(str, str0), contains(str, ty3 ' + tys1), type∃(str, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), ty0 ∈ tys1, ty3 ∈ tys, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ # tys1 .butlast < # tys, tys1 = [], contains(str0, ty, ty0), dups(tys), ty ∈ tys
Proof step 63:
contains(str0, ty3, tys1 .last) ∨ dups(tys1 .butlast) ∨ ty3 ∈ tys1 .butlast, tys + ty0 ' = ty3 ' + tys1, level⊆(str, str0), contains(str, ty3 ' + tys1), type∃(str, ty1), ty1 ≤ ty, is_reftype(ty), type∃(str, ty), ty0 ∈ tys1, ty3 ∈ tys, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ mkfs(class, ty2, fieldvar) ' ∈ instfields(ty1 .class) ∧ ty3 ≤ ty2, is_arraytype(ty1) → ty3 ≤ ty1 .type, ∀ ty0, ty, str0, str, tys0. # tys0 < # tys → (level⊆(str, str0) ∧ contains(str, ty ' + tys0 + ty0 ') → contains(str0, ty, ty0) ∨ dups(tys0) ∨ ty ∈ tys0) ⊦ tys1 = [], contains(str0, ty, ty0), dups(tys), ty ∈ tys

Rule argument

[substlist-arg: [ty0, ty, str0, str, tys0] → [tys1 .last, ty3, str0, str, tys1 .butlast] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : tys ≠ [] ⊦ tys .butlast + tys .last ' = tys], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1])], [EXTRATERMS : (tys1 .last, ty3, str0, str, tys1 .butlast)]]