x1 is a binary operator in space/under conditions/on (or endowing) set x2 such that there is an identity element and for any element for which it is defined in the space (excepting possibly a small number of special elements), there exists at least one element also in the space which is a left-inverse of that element under the operator.
This presupposes sezni. This does not say that the operator has an inverse, merely that each element does under the operator (these properties are closely related though). See also: socni, sezni, cajni, facni.