Assert
Assert, profess, state, affirm, aver, insist, attest, contend, move, make out, asseverate, declare, maintain, hold, avow, protest, swear, argue, submit, allege, avouch, and represent.
Lay claim to
Lay claim to, assert ownership of, pretend to, ask for, put in for, sue for, exact, say that one owns, formally request, request, apply for, put in an application for, and demand.
Assertion
Assertion, profession, avowal, protestation, contention, case, pretence, request, demand, call, declaration, affirmation, averment, representation, submission, allegation, asseveration, application, and petition.