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…endencies of elhf.
tirix
reviewed
Sep 27, 2026
tirix
reviewed
Sep 27, 2026
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| $( Any member of the cumulative hierarchy of sets is well-founded. | ||
| (Contributed by Mario Carneiro, 28-May-2013.) (Revised by Mario | ||
| Carneiro, 16-Nov-2014.) $) | ||
| r1elwf $p |- ( A e. ( R1 ` B ) -> A e. U. ( R1 " On ) ) $= | ||
| ( vx cr1 cfv wcel cv csuc con0 wrex cima cuni cdm wlim word wfun r1funlim | ||
| wss simpri wceq limord ordsson mp2b elfvdm sselid cpw wtr r1tr trss ax-mp | ||
| wi elpwg mpbird r1sucg syl eleqtrrd suceq fveq2d eleq2d rspcev rankwflemb | ||
| syl2anc sylibr ) ABDEZFZACGZHZDEZFZCIJZADIKLFVEBIFABHZDEZFZVJVEDMZIBVNNZV | ||
| NOVNIRDPVOQSVNUAVNUBUCABDUDZUEVEAVDUFZVLVEAVQFAVDRZVDUGVEVRUKBUHVDAUIUJAV | ||
| DVDULUMVEBVNFVLVQTVPBUNUOUPVIVMCBIVFBTZVHVLAVSVGVKDVFBUQURUSUTVBCAVAVC $. | ||
| ( vx cr1 cfv wcel cv csuc con0 wrex cima cuni cdm wlim wss r1dmlim limord | ||
| word ordsson wceq mp2b elfvdm sselid cpw wtr r1tr trss ax-mp elpwg mpbird | ||
| r1sucg syl eleqtrrd suceq fveq2d eleq2d rspcev syl2anc rankwflemb sylibr | ||
| wi ) ABDEZFZACGZHZDEZFZCIJZADIKLFVCBIFABHZDEZFZVHVCDMZIBVLNVLRVLIOPVLQVLS | ||
| UAABDUBZUCVCAVBUDZVJVCAVNFAVBOZVBUEVCVOVABUFVBAUGUHAVBVBUIUJVCBVLFVJVNTVM | ||
| BUKULUMVGVKCBIVDBTZVFVJAVPVEVIDVDBUNUOUPUQURCAUSUT $. |
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Maybe rather "Any stage of the cumulative hierarchy of sets", also here?
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Actually that's the precise confusion I wanted to avoid by clarifying these comments: A is not a stage, but an element of one. Maybe I could write:
Any element of (any stage of) the cumulative hierarchy of sets is well-founded (recall that
U. ( R1 " On )is the class of well-founded sets).
edit: done in b53f20d
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Oh, now I get it.
I think the comment is fine as it is now.
Maybe the explanation could come in the definition of R1, or in r1val:
In the following, we call
( R1 ` A )a stage of the cumulative hierarchy of sets.
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tirix
approved these changes
Sep 28, 2026
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Some axiom savings, streamlinings, and comment edits around the cumulative hierarchy of sets. Best reviewed by commit.