Probably wrong definition of subtyping

[LuKuangChen]

I think = should be => in the following three lines.

z3guide/website/docs-smtlib/01 - logic/05 - Quantifiers.md

Line 21 in 4333097

(= (and (subtype x y) (subtype y z))

z3guide/website/docs-smtlib/01 - logic/05 - Quantifiers.md

Line 27 in 4333097

(= (and (subtype x y) (subtype x z))

z3guide/website/docs-smtlib/01 - logic/05 - Quantifiers.md

Line 30 in 4333097

(= (subtype x y)

Otherwise, the specification prohibits the existence of non-root types. Specifically, the following program (where the only interesting lines are the last three lines) prints sat unsat.

(declare-sort Type)
(declare-fun subtype (Type Type) Bool)
(declare-fun array-of (Type) Type)
(assert (forall ((x Type)) (subtype x x)))
(assert (forall ((x Type) (y Type) (z Type))
          (= (and (subtype x y) (subtype y z)) 
              (subtype x z)))) 
(assert (forall ((x Type) (y Type))
          (= (and (subtype x y) (subtype y x)) 
              (= x y))))
(assert (forall ((x Type) (y Type) (z Type))
          (= (and (subtype x y) (subtype x z)) 
              (or (subtype y z) (subtype z y))))) 
(assert (forall ((x Type) (y Type))
          (= (subtype x y) 
              (subtype (array-of x) (array-of y)))))
(declare-const root-type Type)
(assert (forall ((x Type)) (subtype x root-type)))
(check-sat)
(declare-const another-type Type)
(assert (not (= root-type another-type)))
(check-sat)