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Proof step 6 from proof contains-array (previous step)

type∃(str, mkarraytype(ty)) ∧ is_reftype(mkarraytype(ty)) ∧ (∃ ty1. ty1 ≤ mkarraytype(ty) ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ ty0 ≤ fs .type)) ∧ (is_arraytype(ty1) → ty0 ≤ ty1 .type) ∧ contains(str, ty0 ' + tys0)) ⊦ contains(str, ty ' + tys0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
type∃(str, ty1), contains(str, ty0 ' + tys0), type∃(str, ty), is_arraytype(ty1), ty1 .type ≤ ty, ty0 ≤ ty1 .type, ty0 ≤ ty ⊦ contains(str, ty ' + tys0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ ty ≤ ty0 ∧ ty0 ≤ ty1 → ty ≤ ty1], [CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ is_reftype(mkarraytype(ty))], [CSIMPSEQ : ⊦ type∃(str, mkarraytype(ty)) ↔ type∃(str, ty)])]]