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Proof step 10 from proof contains-trans-01 (previous step)

contains(str, ty0 ' + tys0 + ty1 '), type∃(str, ty), is_reftype(ty), ty2 ≤ ty, type∃(str, ty2), contains(str, (ty3 ' + tys2) + ty0 '), 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 < # (ty3 + tys2) → (contains(str, ty0 ' + tys0 + ty1 ') ∧ contains(str, ty ' + tys1 + ty0 ') → contains(str, ty ' + tys1 + ty0 ' + tys0 + ty1 ')) ⊦ contains(str, (ty3 ' + tys2) + ty0 ' + tys0 + ty1 ')

User applied rule apply induction

And closed the goal!

Rule argument

[substlist-arg: [ty, ty1, tys0, ty0, str, tys1] → [ty3, ty1, tys0, ty0, str, tys2] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty + tys = ty ' + tys], [CSIMPSEQ : ⊦ # (tys + tys0) = # tys + # tys0], [CSIMPSEQ : ⊦ # ty ' = 0 +1], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ ¬ n < n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (ty3, ty1, tys0, ty0, str, tys2)]]