See tlm's reply above. use is impicitly wrapped in a BEGIN. And since BEGIN's have no precedence over each other, your second example is effectively: 
BEGIN {
  require mylib1;
  mylib1->import();
  unshift (@INC,"\\mylib");
}

[download]
(I left out 'use strict' for simplicity's sake).

In reply to Re^2: What is the scope of BEGIN? Or... when does it "begin?" by Mutant
in thread What is the scope of BEGIN? Or... when does it "begin?" by argv

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