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Proof step 4 from proof contains-field-def-case (previous step)

tys0 = [], type∃(str, ty), ty0 ≤ ty, contains(str, ty0 ' + tys0), is_reftype((ty0 ' + tys0) .last), is_classtype((ty0 ' + tys0) .last) → ¬ interface∃(str, (ty0 ' + tys0) .last .class) ∧ fs ' ∈ instfields((ty0 ' + tys0) .last .class), is_arraytype((ty0 ' + tys0) .last) → fs ' = _length ⊦ ∃ ty1. (ty1 ≤ ty ∧ type∃(str, ty1) ∨ contains(str, ty, ty1)) ∧ is_reftype(ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ fs ' ∈ instfields(ty1 .class)) ∧ (is_arraytype(ty1) → fs ' = _length)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ contains(str, ty ') ↔ type∃(str, ty)
Proof step 3:
type∃(str, ty), ty0 ≤ ty, type∃(str, ty0), is_reftype(ty0), is_classtype(ty0) → ¬ interface∃(str, ty0 .class) ∧ fs ' ∈ instfields(ty0 .class), is_arraytype(ty0) → fs ' = _length ⊦ ∃ ty1. (ty1 ≤ ty ∧ type∃(str, ty1) ∨ contains(str, ty, ty1)) ∧ is_reftype(ty1) ∧ (is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ fs ' ∈ instfields(ty1 .class)) ∧ (is_arraytype(ty1) → fs ' = _length)

Rule argument

[emptyarg]

Additional information

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