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Proof step 9 from proof contains-boolarray (previous step)

tys + ty ' ≠ [] ⊦ type∃(str, mkarraytype(boolean_type)) ∧ is_reftype(mkarraytype(boolean_type)) ∧ (∃ ty1. ty1 ≤ mkarraytype(boolean_type) ∧ type∃(str, ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ (∃ fs. fs ' ∈ instfields(ty1 .class) ∧ (tys + ty ') .first ≤ fs .type)) ∧ (is_arraytype(ty1) → (tys + ty ') .first ≤ ty1 .type) ∧ contains(str, tys + ty ')) ↔ tys = [] ∧ ty = boolean_type

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ (∃ ty0. is_arraytype(ty0) ∧ ty0 .type = boolean_type ∧ type∃(str, ty0) ∧ (tys + ty ') .first ≤ ty0 .type ∧ contains(str, tys + ty ')) ↔ tys = [] ∧ ty = boolean_type

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (tys + tys0) + tys1 = tys + tys0 + tys1], [CSIMPSEQ : ⊦ tys + ty ' ≠ []], [CSIMPSEQ : ⊦ is_arraytype(ty) → ¬ is_classtype(ty)], [CSIMPSEQ : ⊦ ty ≤ boolean_type ↔ ty = boolean_type], [CSIMPSEQ : ⊦ ty0 ≤ mkarraytype(ty) ↔ is_arraytype(ty0) ∧ ty0 .type ≤ ty], [CSIMPSEQ : ⊦ is_reftype(mkarraytype(ty))], [CSIMPSEQ : ⊦ type∃(str, boolean_type)], [CSIMPSEQ : ⊦ type∃(str, mkarraytype(ty)) ↔ type∃(str, ty)])]]