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Proof step 24 from proof contains-trans-01 (previous step)

tys + ty0 ' + tys0 + ty1 ' ≠ [], contains(str, ty ' + tys + ty0 '), contains(str, ty0 ' + tys0 + ty1 '), ∀ 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 ')) ⊦ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty2. ty2 ≤ ty ∧ type∃(str, ty2) ∧ (is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ (∃ fs. fs ' ∈ instfields(ty2 .class) ∧ (tys + ty0 ' + tys0 + ty1 ') .first ≤ fs .type)) ∧ (is_arraytype(ty2) → (tys + ty0 ' + tys0 + ty1 ') .first ≤ ty2 .type) ∧ contains(str, tys + ty0 ' + tys0 + ty1 '))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
contains(str, ty ' + tys + ty0 '), contains(str, ty0 ' + tys0 + ty1 '), ∀ 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 ')) ⊦ type∃(str, ty) ∧ is_reftype(ty) ∧ (∃ ty2. ty2 ≤ ty ∧ type∃(str, ty2) ∧ (is_classtype(ty2) → ¬ interface∃(str, ty2 .class) ∧ (∃ fs. fs ' ∈ instfields(ty2 .class) ∧ (tys + ty0 ') .first ≤ fs .type)) ∧ (is_arraytype(ty2) → (tys + ty0 ') .first ≤ ty2 .type) ∧ contains(str, tys + ty0 ' + tys0 + ty1 '))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (tys + ty ' + tys0) .first = (tys + ty ') .first], [CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ tys + ty ' ≠ []])]]