x_{1} is a strict/proper sub-x_{2} [structure] in/of x_{3}; x_{2} is a structure and x_{1} and x_{3} are both examples of that structure x_{2} such that x_{1} is entirely contained within x_{3} (where containment is defined according to the standard/characteristics/definition of x_{2}; but in any case, no member/part/element that belongs to x_{1} does not also belong to x_{3}), but there is some member/part/element of x_{3} that does not belong to x_{1} in the same way.

If x2 is a (sub)set, then x1 is a proper subset of x3; if x2 is a mathematical/algebraic (sub)group, then x1 is a proper subgroup of x3; etc. Can also be used for describing proper sub-lakes (such as Lake Michigan), proper super-selma'o, and other non-mathmetical usages. x3 is a proper super-x2 of/with x1. Biological taxa, if comparable, are usually/hypothetically proper. See also: klesi, enklesi, cletu, cmeta.

- enklesi
- x
_{1}is an (arbitrary) x_{2}-set (li) of superset x_{3}; x_{1}is subset/subgroup/subcategory/subclass/vel sim. of x_{3}with cardinality/size x_{2}. - trajmaumce
- x
_{1}(li) is an extremal bound (supremum/infimum/possibly-unattained extremum (loose sense in English)/asymptote (one sense)/best possible bound (one sense)) on set x_{2}(set) in direction x_{3}(li) in ordered structure x_{4}; x_{1}bounds x_{2}tightly/maximally-strongly from the x_{3}side in x_{4}; x_{2}is bounded from the x_{3}side by x_{1}and any other bound on that side is worse than is x_{1}. - tsekane
- x
_{1}(linear manifold, vector, etc.) is/lies secant to x_{2}(object, surface, curve, manifold, etc.) passing through or toward points/loci x_{3}(set of intersected points), by standard/definition/in system x_{4}. - zmaumce
- x
_{1}(li) is a bound on set x_{2}(set) in direction x_{3}(li) in ordered structure x_{4}; x_{1}bounds x_{2}from the x_{3}side in x_{4}; x_{2}is bounded from the x_{3}side by x_{1}.