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Proof step 49 from proof contains-field-def-case (previous step)

tys0 = ty2 + tys, type∃(str, ty), ty0 ≤ ty, type∃(str, ty0), is_reftype(ty0), ty1 ≤ ty0, type∃(str, ty1), contains(str, tys0), is_reftype(tys0 .last), ty1 ≤ ty, is_arraytype(ty1) → ty2 ≤ ty1 .type, is_classtype(tys0 .last) → ¬ interface∃(str, tys0 .last .class) ∧ fs ' ∈ instfields(tys0 .last .class), is_arraytype(tys0 .last) → fs ' = _length, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ fs0 ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs0 .type ⊦ tys0 = [], contains(str, ty ' + tys0), tys0 .last ≤ ty ∧ type∃(str, tys0 .last)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
ty1 ≤ ty, type∃(str, ty), ty0 ≤ ty, type∃(str, ty0), is_reftype(ty0), ty1 ≤ ty0, type∃(str, ty1), contains(str, ty2 ' + tys), is_reftype((ty2 ' + tys) .last), is_arraytype(ty1) → ty2 ≤ ty1 .type, is_classtype(ty1) → ¬ interface∃(str, ty1 .class) ∧ fs0 ' ∈ instfields(ty1 .class) ∧ ty2 ≤ fs0 .type, is_classtype((ty2 ' + tys) .last) → ¬ interface∃(str, (ty2 ' + tys) .last .class) ∧ fs ' ∈ instfields((ty2 ' + tys) .last .class), is_arraytype((ty2 ' + tys) .last) → fs ' = _length ⊦ contains(str, ty ' + ty2 ' + tys), (ty2 ' + tys) .last ≤ ty ∧ type∃(str, (ty2 ' + tys) .last)

Rule argument

[emptyarg]

Additional information

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