P. 359 of Theorem List - Metamath Proof Explorer

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**Theorem List for Metamath Proof Explorer -** 35801-35900 *Has distinct variable group(s)
Type	Label	Description
Statement

Theorem	cdlemeg46c 35801*	TODO FIX COMMENT. (Contributed by NM, 1-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemeg46rvOLDN 35802*	Value of g_s(r) when r is an atom under pq and s is any atom not under pq, using very compact hypotheses. TODO FIX COMMENT. (Contributed by NM, 3-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$

Theorem	cdlemeg46rv2OLDN 35803*	Value of g_s(r) when r is an atom under pq and s is any atom not under pq, using very compact hypotheses. TODO FIX COMMENT. (Contributed by NM, 3-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$

Theorem	cdlemeg46fvaw 35804*	Show that is an atom not under when is an atom not under . (Contributed by NM, 1-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemeg46nlpq 35805*	Show that is not under $.\/$ when isn't. (Contributed by NM, 3-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemeg46ngfr 35806*	TODO FIX COMMENT g(f(s))=s p. 115 4th line from bottom. (Contributed by NM, 4-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemeg46nfgr 35807*	TODO FIX COMMENT f(g(s))=s p. 115 antepenultimate line. (Contributed by NM, 4-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemeg46sfg 35808*	TODO FIX COMMENT f(r) $\/$ s = f(r) $\/$ g(s) p. 116 2nd line TODO: eliminate eqcomd? (Contributed by NM, 4-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $.\/$

Theorem	cdlemeg46fjgN 35809*	NOT NEEDED? TODO FIX COMMENT. TODO eliminate eqcomd 2628? p. 116 2nd line. (Contributed by NM, 2-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $.\/$

Theorem	cdlemeg46rjgN 35810*	NOT NEEDED? TODO FIX COMMENT. r $\/$ g(s) = r $\/$ v₂ p. 115 last line. (Contributed by NM, 2-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $.\/$

Theorem	cdlemeg46fjv 35811*	TODO FIX COMMENT f(r) $\/$ f(g(s)) = f(r) $\/$ v₂ p. 116 2nd line. (Contributed by NM, 2-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $.\/$

Theorem	cdlemeg46fsfv 35812*	TODO FIX COMMENT f(r) $\/$ s = f(r) $\/$ v₂ p. 116 2nd line. (Contributed by NM, 2-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $.\/$

Theorem	cdlemeg46frv 35813*	TODO FIX COMMENT. (f(r) $\/$ v₂) $/\$ w = v₂ p. 116 3rd line. (Contributed by NM, 2-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$

Theorem	cdlemeg46v1v2 35814*	TODO FIX COMMENT v₁ = v₂ p. 116 3rd line. (Contributed by NM, 2-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$

Theorem	cdlemeg46vrg 35815*	TODO FIX COMMENT v₁ r $\/$ g(s) p. 116 3rd line. (Contributed by NM, 3-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$

Theorem	cdlemeg46rgv 35816*	TODO FIX COMMENT r g(s) $\/$ v₁ p. 116 3rd line. (Contributed by NM, 3-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$

Theorem	cdlemeg46req 35817*	TODO FIX COMMENT r = (v₁ $\/$ g(s)) p. 116 3rd line. (Contributed by NM, 3-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemeg46gfv 35818*	TODO FIX COMMENT p. 115 penultimate line: g(f(r)) = (p v q) ^ (g(s) v v₁). (Contributed by NM, 4-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemeg46gfr 35819*	TODO FIX COMMENT p. 116 penultimate line: g(f(r)) = r. (Contributed by NM, 4-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$

Theorem	cdlemeg46gfre 35820*	TODO FIX COMMENT p. 116 penultimate line: g(f(r)) = r. (Contributed by NM, 4-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemeg46gf 35821*	TODO FIX COMMENT Eliminate antecedent $.\/$ . (Contributed by NM, 4-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemeg46fgN 35822*	TODO FIX COMMENT p. 116 penultimate line: f(g(r)) = r. (Contributed by NM, 4-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme48d 35823*	TODO: fix comment. (Contributed by NM, 8-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$

Theorem	cdleme48gfv1 35824*	TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme48gfv 35825*	TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme48fgv 35826*	TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemeg49lebilem 35827*	Part of proof of Lemma D in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50lebi 35828*	Part of proof of Lemma D in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50eq 35829*	Part of proof of Lemma D in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50f 35830*	Part of proof of Lemma D in [Crawley] p. 113. TODO: fix comment. TODO: can we use just since range is computed in cdleme50rn 35833? (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50f1 35831*	Part of proof of Lemma D in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50rnlem 35832*	Part of proof of Lemma D in [Crawley] p. 113. TODO: fix comment. TODO: can we get rid of stuff if we show earlier? (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50rn 35833*	Part of proof of Lemma D in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50f1o 35834*	Part of proof of Lemma D in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50laut 35835*	Part of proof of Lemma D in [Crawley] p. 113. is a lattice automorphism. TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50ldil 35836*	Part of proof of Lemma D in [Crawley] p. 113. is a lattice dilation. TODO: fix comment. (Contributed by NM, 9-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50trn1 35837*	Part of proof that is a translation. $.\/$ case. TODO: fix comment. (Contributed by NM, 10-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $./\$

Theorem	cdleme50trn2a 35838*	Part of proof that is a translation. $.\/$ case. TODO: fix comment. (Contributed by NM, 10-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$

Theorem	cdleme50trn2 35839*	Part of proof that is a translation. Remove hypotheses no longer needed from cdleme50trn2a 35838. TODO: fix comment. (Contributed by NM, 10-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $./\$

Theorem	cdleme50trn12 35840*	Part of proof that is a translation. Combine $.\/$ and $.\/$ cases. TODO: fix comment. (Contributed by NM, 10-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$

Theorem	cdleme50trn3 35841*	Part of proof that is a translation. case. TODO: fix comment. (Contributed by NM, 10-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$

Theorem	cdleme50trn123 35842*	Part of proof that is a translation. Combine all cases. TODO: fix comment. (Contributed by NM, 10-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$

Theorem	cdleme51finvfvN 35843*	Part of proof of Lemma E in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 14-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme51finvN 35844*	Part of proof of Lemma E in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 14-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50ltrn 35845*	Part of proof of Lemma E in [Crawley] p. 113. is a lattice translation. TODO: fix comment. (Contributed by NM, 10-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme51finvtrN 35846*	Part of proof of Lemma E in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 14-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme50ex 35847*	Part of Lemma E in [Crawley] p. 113. TODO: fix comment. (Contributed by NM, 11-Apr-2013.)
$/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdleme 35848*	Lemma E in [Crawley] p. 113. If p,q are atoms not under hyperplane w, then there is a unique translation f such that f(p) = q. (Contributed by NM, 11-Apr-2013.)
$/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemf1 35849*	Part of Lemma F in [Crawley] p. 116. TODO: should this or part of it become a stand-alone theorem? (Contributed by NM, 12-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemf2 35850*	Part of Lemma F in [Crawley] p. 116. (Contributed by NM, 12-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$

Theorem	cdlemf 35851*	Lemma F in [Crawley] p. 116. If u is an atom under w, there exists a translation whose trace is u. (Contributed by NM, 12-Apr-2013.)
$/\$ $/\$ $/\$

Theorem	cdlemfnid 35852*	cdlemf 35851 with additional constraint of non-identity. (Contributed by NM, 20-Jun-2013.)
$/\$ $/\$ $/\$ $/\$

Theorem	cdlemftr3 35853*	Special case of cdlemf 35851 showing existence of non-identity translation with trace different from any 3 given lattice elements. (Contributed by NM, 24-Jul-2013.)
$/\$ $/\$ $/\$ $/\$

Theorem	cdlemftr2 35854*	Special case of cdlemf 35851 showing existence of non-identity translation with trace different from any 2 given lattice elements. (Contributed by NM, 25-Jul-2013.)
$/\$ $/\$ $/\$

Theorem	cdlemftr1 35855*	Part of proof of Lemma G of [Crawley] p. 116, sixth line of third paragraph on p. 117: there is "a translation h, different from the identity, such that tr h tr f." (Contributed by NM, 25-Jul-2013.)
$/\$ $/\$

Theorem	cdlemftr0 35856*	Special case of cdlemf 35851 showing existence of a non-identity translation. (Contributed by NM, 1-Aug-2013.)
$/\$

Theorem	trlord 35857*	The ordering of two Hilbert lattice elements (under the fiducial hyperplane ) is determined by the translations whose traces are under them. (Contributed by NM, 3-Mar-2014.)
$/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1a 35858*	Shorter expression for . TODO: fix comment. TODO: shorten using cdleme 35848 or vice-versa? Also, if not shortened with cdleme 35848, then it can be moved up to save repeating hypotheses. (Contributed by NM, 15-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1b2 35859*	This theorem can be used to shorten hypothesis. TODO: Fix comment. (Contributed by NM, 18-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1idlemN 35860*	Lemma for cdlemg1idN 35865. (Contributed by NM, 18-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1fvawlemN 35861*	Lemma for ltrniotafvawN 35866. (Contributed by NM, 18-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1ltrnlem 35862*	Lemma for ltrniotacl 35867. (Contributed by NM, 18-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1finvtrlemN 35863*	Lemma for ltrniotacnvN 35868. (Contributed by NM, 18-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1bOLDN 35864*	This theorem can be used to shorten hypothesis that have the form of the conclusion. TODO: fix comment. (Contributed by NM, 16-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$

Theorem	cdlemg1idN 35865*	Version of cdleme31id 35682 with simpler hypotheses. TODO: Fix comment. (Contributed by NM, 18-Apr-2013.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	ltrniotafvawN 35866*	Version of cdleme46fvaw 35789 with simpler hypotheses. TODO: Fix comment. (Contributed by NM, 18-Apr-2013.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	ltrniotacl 35867*	Version of cdleme50ltrn 35845 with simpler hypotheses. TODO: Fix comment. (Contributed by NM, 17-Apr-2013.)
$/\$ $/\$ $/\$ $/\$ $/\$

Theorem	ltrniotacnvN 35868*	Version of cdleme51finvtrN 35846 with simpler hypotheses. TODO: Fix comment. (Contributed by NM, 18-Apr-2013.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$

Theorem	ltrniotaval 35869*	Value of the unique translation specified by a value. (Contributed by NM, 21-Feb-2014.)
$/\$ $/\$ $/\$ $/\$ $/\$

Theorem	ltrniotacnvval 35870*	Converse value of the unique translation specified by a value. (Contributed by NM, 21-Feb-2014.)
$/\$ $/\$ $/\$ $/\$ $/\$

Theorem	ltrniotaidvalN 35871*	Value of the unique translation specified by identity value. (Contributed by NM, 25-Aug-2014.) (New usage is discouraged.)
$/\$ $/\$ $/\$

Theorem	ltrniotavalbN 35872*	Value of the unique translation specified by a value. (Contributed by NM, 10-Mar-2014.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemeiota 35873*	A translation is uniquely determined by one of its values. (Contributed by NM, 18-Apr-2013.)
$/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1ci2 35874*	Any function of the form of the function constructed for cdleme 35848 is a translation. TODO: Fix comment. (Contributed by NM, 18-Apr-2013.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1cN 35875*	Any translation belongs to the set of functions constructed for cdleme 35848. TODO: Fix comment. (Contributed by NM, 18-Apr-2013.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg1cex 35876*	Any translation is one of our s. TODO: fix comment, move to its own block maybe? Would this help for cdlemf 35851? (Contributed by NM, 17-Apr-2013.)
$/\$ $/\$ $/\$

Theorem	cdlemg2cN 35877*	Any translation belongs to the set of functions constructed for cdleme 35848. TODO: Fix comment. (Contributed by NM, 22-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg2dN 35878*	This theorem can be used to shorten hypothesis. TODO: Fix comment. (Contributed by NM, 21-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg2cex 35879*	Any translation is one of our s. TODO: fix comment, move to its own block maybe? Would this help for cdlemf 35851? (Contributed by NM, 22-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$

Theorem	cdlemg2ce 35880*	Utility theorem to eliminate p,q when converting theorems with explicit f. TODO: fix comment. (Contributed by NM, 22-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg2jlemOLDN 35881*	Part of proof of Lemma E in [Crawley] p. 113. TODO: FIX COMMENT. f preserves join: f(r $\/$ s) = f(r) $\/$ s, p. 115 10th line from bottom. TODO: Combine with cdlemg2jOLDN 35886? (Contributed by NM, 22-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg2fvlem 35882*	Lemma for cdlemg2fv 35887. (Contributed by NM, 23-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg2klem 35883*	cdleme42keg 35774 with simpler hypotheses. TODO: FIX COMMENT. (Contributed by NM, 22-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg2idN 35884	Version of cdleme31id 35682 with simpler hypotheses. TODO: Fix comment. (Contributed by NM, 21-Apr-2013.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg3a 35885	Part of proof of Lemma G in [Crawley] p. 116, line 19. Show p $\/$ q = p $\/$ u. TODO: reformat cdleme0cp 35501 to match this, then replace with cdleme0cp 35501. (Contributed by NM, 19-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg2jOLDN 35886	TODO: Replace this with ltrnj 35418. (Contributed by NM, 22-Apr-2013.) (New usage is discouraged.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg2fv 35887	Value of a translation in terms of an associated atom. cdleme48fvg 35788 with simpler hypotheses. TODO: Use ltrnj 35418 to vastly simplify. (Contributed by NM, 23-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg2fv2 35888	Value of a translation in terms of an associated atom. TODO: FIX COMMENT. TODO: Is this useful elsewhere e.g. around cdlemeg46fjv 35811 that use more complex proofs? TODO: Use ltrnj 35418 to vastly simplify. (Contributed by NM, 23-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg2k 35889	cdleme42keg 35774 with simpler hypotheses. TODO: FIX COMMENT. TODO: derive from cdlemg3a 35885, cdlemg2fv2 35888, cdlemg2jOLDN 35886, ltrnel 35425? (Contributed by NM, 22-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg2kq 35890	cdlemg2k 35889 with and swapped. TODO: FIX COMMENT. (Contributed by NM, 15-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg2l 35891	TODO: FIX COMMENT. (Contributed by NM, 23-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg2m 35892	TODO: FIX COMMENT. (Contributed by NM, 25-Apr-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$

Theorem	cdlemg5 35893*	TODO: Is there a simpler more direct proof, that could be placed earlier e.g. near lhpexle 35291? TODO: The $.\/$ hypothesis is unused. FIX COMMENT. (Contributed by NM, 26-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemb3 35894*	Given two atoms not under the fiducial co-atom , there is a third. Lemma B in [Crawley] p. 112. TODO: Is there a simpler more direct proof, that could be placed earlier e.g. near lhpexle 35291? Then replace cdlemb2 35327 with it. This is a more general version of cdlemb2 35327 without condition. (Contributed by NM, 27-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg7fvbwN 35895	Properties of a translation of an element not under . TODO: Fix comment. Can this be simplified? Perhaps derived from cdleme48bw 35790? Done with a ltrn theorem? (Contributed by NM, 28-Apr-2013.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg4a 35896	TODO: FIX COMMENT If fg(p) = p, then tr f = tr g. (Contributed by NM, 23-Apr-2013.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg4b1 35897	TODO: FIX COMMENT. (Contributed by NM, 24-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg4b2 35898	TODO: FIX COMMENT. (Contributed by NM, 24-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg4b12 35899	TODO: FIX COMMENT. (Contributed by NM, 24-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg4c 35900	TODO: FIX COMMENT. (Contributed by NM, 24-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

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20501-20600 207 20601-20700 208 20701-20800 209 20801-20900 210 20901-21000 211 21001-21100 212 21101-21200 213 21201-21300 214 21301-21400 215 21401-21500 216 21501-21600 217 21601-21700 218 21701-21800 219 21801-21900 220 21901-22000 221 22001-22100 222 22101-22200 223 22201-22300 224 22301-22400 225 22401-22500 226 22501-22600 227 22601-22700 228 22701-22800 229 22801-22900 230 22901-23000 231 23001-23100 232 23101-23200 233 23201-23300 234 23301-23400 235 23401-23500 236 23501-23600 237 23601-23700 238 23701-23800 239 23801-23900 240 23901-24000 241 24001-24100 242 24101-24200 243 24201-24300 244 24301-24400 245 24401-24500 246 24501-24600 247 24601-24700 248 24701-24800 249 24801-24900 250 24901-25000 251 25001-25100 252 25101-25200 253 25201-25300 254 25301-25400 255 25401-25500 256 25501-25600 257 25601-25700 258 25701-25800 259 25801-25900 260 25901-26000 261 26001-26100 262 26101-26200 263 26201-26300 264 26301-26400 265 26401-26500 266 26501-26600 267 26601-26700 268 26701-26800 269 26801-26900 270 26901-27000 271 27001-27100 272 27101-27200 273 27201-27300 274 27301-27400 275 27401-27500 276 27501-27600 277 27601-27700 278 27701-27800 279 27801-27900 280 27901-28000 281 28001-28100 282 28101-28200 283 28201-28300 284 28301-28400 285 28401-28500 286 28501-28600 287 28601-28700 288 28701-28800 289 28801-28900 290 28901-29000 291 29001-29100 292 29101-29200 293 29201-29300 294 29301-29400 295 29401-29500 296 29501-29600 297 29601-29700 298 29701-29800 299 29801-29900 300 29901-30000 301 30001-30100 302 30101-30200 303 30201-30300 304 30301-30400 305 30401-30500 306 30501-30600 307 30601-30700 308 30701-30800 309 30801-30900 310 30901-31000 311 31001-31100 312 31101-31200 313 31201-31300 314 31301-31400 315 31401-31500 316 31501-31600 317 31601-31700 318 31701-31800 319 31801-31900 320 31901-32000 321 32001-32100 322 32101-32200 323 32201-32300 324 32301-32400 325 32401-32500 326 32501-32600 327 32601-32700 328 32701-32800 329 32801-32900 330 32901-33000 331 33001-33100 332 33101-33200 333 33201-33300 334 33301-33400 335 33401-33500 336 33501-33600 337 33601-33700 338 33701-33800 339 33801-33900 340 33901-34000 341 34001-34100 342 34101-34200 343 34201-34300 344 34301-34400 345 34401-34500 346 34501-34600 347 34601-34700 348 34701-34800 349 34801-34900 350 34901-35000 351 35001-35100 352 35101-35200 353 35201-35300 354 35301-35400 355 35401-35500 356 35501-35600 357 35601-35700 358 35701-35800 359 35801-35900 360 35901-36000 361 36001-36100 362 36101-36200 363 36201-36300 364 36301-36400 365 36401-36500 366 36501-36600 367 36601-36700 368 36701-36800 369 36801-36900 370 36901-37000 371 37001-37100 372 37101-37200 373 37201-37300 374 37301-37400 375 37401-37500 376 37501-37600 377 37601-37700 378 37701-37800 379 37801-37900 380 37901-38000 381 38001-38100 382 38101-38200 383 38201-38300 384 38301-38400 385 38401-38500 386 38501-38600 387 38601-38700 388 38701-38800 389 38801-38900 390 38901-39000 391 39001-39100 392 39101-39200 393 39201-39300 394 39301-39400 395 39401-39500 396 39501-39600 397 39601-39700 398 39701-39800 399 39801-39900 400 39901-40000 401 40001-40100 402 40101-40200 403 40201-40300 404 40301-40400 405 40401-40500 406 40501-40600 407 40601-40700 408 40701-40800 409 40801-40900 410 40901-41000 411 41001-41100 412 41101-41200 413 41201-41300 414 41301-41400 415 41401-41500 416 41501-41600 417 41601-41700 418 41701-41800 419 41801-41900 420 41901-42000 421 42001-42100 422 42101-42200 423 42201-42300 424 42301-42400 425 42401-42500 426 42501-42551

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