There was no system 7.1.3 ever, that is only Finder version, like there is 7.1.4 too. System and Finder never shared the same release number except from 7.0 to 7.1
See here: http://support.apple.com/kb/TA31885?viewlocale=en_US

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Thanks. Deep down, I thought the PowerBook 500-series was 7.1.1; but when I saw 7.1.3 on the Finder, I suppose I assumed that it was 7.1.3...

I knew that the 7.1.2's were really 7.1.2 not 7.1.4.