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Proof step 13 from proof contains-trans-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
contains(str, ty0 ' + tys0 + ty1 '), type∃(str, ty), is_reftype(ty), ty2 ≤ ty, type∃(str, ty2), contains(str, tys + ty0 '), is_arraytype(ty2) → tys .first ≤ ty2 .type, is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ mkfs(class, ty4, fieldvar) ' ∈ instfields(ty2 .class) ∧ tys .first ≤ 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 ')) ⊦ tys = [], contains(str, tys + ty0 ' + tys0 + ty1 ')

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ tys .first ∈ tys ↔ tys ≠ []], [CSIMPSEQ : ⊦ ty ∈ ty0 ' ↔ ty = ty0], [CSIMPSEQ : ⊦ ty ∈ tys + tys0 ↔ ¬ ¬ (ty ∈ tys ∨ ty ∈ tys0)], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ tys ≠ [] → tys .first ' + tys .rest = tys])]]