<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class=""><div><blockquote type="cite" class=""><div class="">On 25 Aug 2017, at 20:14, Viorel Preoteasa <<a href="mailto:viorel.preoteasa@aalto.fi" class="">viorel.preoteasa@aalto.fi</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><span style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">One possible solution:</span><br style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><br style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">Add the new class in Complete_Lattice.thy, replacing the existing class</span><br style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><br style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">Prove the instantiations and the complete_linearord subclass later</span><br style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">in Hilbert_Choice.</span><br style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><br class=""><span style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">On the other hand, it seems inconvenient to have the Hilbert Choice</span><br style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><span style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;" class="">to depend on so many other theories.</span><br style="font-family: Consolas; font-size: 13px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""></div></blockquote></div><br class=""><div class="">I’d prefer this provided the instantiations aren’t needed earlier.</div><div class=""><br class=""></div><div class="">The delay in the introduction of the Axiom of Choice is partly historical, but it’s worth noting how much of HOL can be developed without it. </div><div class=""><br class=""></div><div class="">Larry</div></body></html>