P. 360 of Theorem List - Metamath Proof Explorer

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**Theorem List for Metamath Proof Explorer -** 35901-36000 *Has distinct variable group(s)
Type	Label	Description
Statement

Theorem	cdlemg4d 35901	TODO: FIX COMMENT. (Contributed by NM, 25-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$

Theorem	cdlemg4e 35902	TODO: FIX COMMENT. (Contributed by NM, 25-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$

Theorem	cdlemg4f 35903	TODO: FIX COMMENT. (Contributed by NM, 25-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$

Theorem	cdlemg4g 35904	TODO: FIX COMMENT. (Contributed by NM, 25-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $./\$ $.\/$

Theorem	cdlemg4 35905	TODO: FIX COMMENT. (Contributed by NM, 25-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$

Theorem	cdlemg6a 35906*	TODO: FIX COMMENT. TODO: replace with cdlemg4 35905. (Contributed by NM, 27-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$

Theorem	cdlemg6b 35907*	TODO: FIX COMMENT. TODO: replace with cdlemg4 35905. (Contributed by NM, 27-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$

Theorem	cdlemg6c 35908*	TODO: FIX COMMENT. (Contributed by NM, 27-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg6d 35909*	TODO: FIX COMMENT. (Contributed by NM, 27-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg6e 35910	TODO: FIX COMMENT. (Contributed by NM, 27-Apr-2013.)
$.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$

Theorem	cdlemg6 35911	TODO: FIX COMMENT. (Contributed by NM, 27-Apr-2013.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg7fvN 35912	Value of a translation composition in terms of an associated atom. (Contributed by NM, 28-Apr-2013.) (New usage is discouraged.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg7aN 35913	TODO: FIX COMMENT. (Contributed by NM, 28-Apr-2013.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg7N 35914	TODO: FIX COMMENT. (Contributed by NM, 28-Apr-2013.) (New usage is discouraged.)
$/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg8a 35915	TODO: FIX COMMENT. (Contributed by NM, 29-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg8b 35916	TODO: FIX COMMENT. (Contributed by NM, 29-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $.\/$

Theorem	cdlemg8c 35917	TODO: FIX COMMENT. (Contributed by NM, 29-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $.\/$

Theorem	cdlemg8d 35918	TODO: FIX COMMENT. (Contributed by NM, 29-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg8 35919	TODO: FIX COMMENT. (Contributed by NM, 29-Apr-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg9a 35920	TODO: FIX COMMENT. (Contributed by NM, 1-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$

Theorem	cdlemg9b 35921	The triples and are centrally perspective. TODO: FIX COMMENT. (Contributed by NM, 1-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$

Theorem	cdlemg9 35922	The triples and are axially perspective by dalaw 35172. Part of Lemma G of [Crawley] p. 116, last 2 lines. TODO: FIX COMMENT. (Contributed by NM, 1-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemg10b 35923	TODO: FIX COMMENT. TODO: Can this be moved up as a stand-alone theorem in ltrn* area? (Contributed by NM, 4-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg10bALTN 35924	TODO: FIX COMMENT. TODO: Can this be moved up as a stand-alone theorem in ltrn* area? TODO: Compare this proof to cdlemg2m 35892 and pick best, if moved to ltrn* area. (Contributed by NM, 4-May-2013.) (New usage is discouraged.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg11a 35925	TODO: FIX COMMENT. (Contributed by NM, 4-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg11aq 35926	TODO: FIX COMMENT. TODO: can proof using this be restructured to use cdlemg11a 35925? (Contributed by NM, 4-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg10c 35927	TODO: FIX COMMENT. TODO: Can this be moved up as a stand-alone theorem in trl* area? (Contributed by NM, 4-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg10a 35928	TODO: FIX COMMENT. (Contributed by NM, 3-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$

Theorem	cdlemg10 35929	TODO: FIX COMMENT. (Contributed by NM, 4-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemg11b 35930	TODO: FIX COMMENT. (Contributed by NM, 5-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$

Theorem	cdlemg12a 35931	TODO: FIX COMMENT. (Contributed by NM, 5-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$

Theorem	cdlemg12b 35932	The triples and are centrally perspective. TODO: FIX COMMENT. (Contributed by NM, 5-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$

Theorem	cdlemg12c 35933	The triples and are axially perspective by dalaw 35172. TODO: FIX COMMENT. (Contributed by NM, 5-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemg12d 35934	TODO: FIX COMMENT. (Contributed by NM, 5-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemg12e 35935	TODO: FIX COMMENT. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $./\$ $.\/$

Theorem	cdlemg12f 35936	TODO: FIX COMMENT. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$

Theorem	cdlemg12g 35937	TODO: FIX COMMENT. TODO: Combine with cdlemg12f 35936. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$

Theorem	cdlemg12 35938	TODO: FIX COMMENT. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg13a 35939	TODO: FIX COMMENT. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $.\/$

Theorem	cdlemg13 35940	TODO: FIX COMMENT. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg14f 35941	TODO: FIX COMMENT. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg14g 35942	TODO: FIX COMMENT. (Contributed by NM, 22-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg15a 35943	Eliminate the condition from cdlemg13 35940. TODO: FIX COMMENT. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg15 35944	Eliminate the $.\/$ $.\/$ condition from cdlemg13 35940. TODO: FIX COMMENT. (Contributed by NM, 25-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg16 35945	Part of proof of Lemma G of [Crawley] p. 116; 2nd line p. 117, which says that (our) cdlemg10 35929 "implies (2)" (of p. 116). No details are provided by the authors, so there may be a shorter proof; but ours requires the 14 lemmas, one using Desargues' law dalaw 35172, in order to make this inference. This final step eliminates the condition from cdlemg12 35938. TODO: FIX COMMENT. TODO: should we also eliminate here (or earlier)? Do it if we don't need to add it in for something else later. (Contributed by NM, 6-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg16ALTN 35946	This version of cdlemg16 35945 uses cdlemg15a 35943 instead of cdlemg15 35944, in case cdlemg15 35944 ends up not being needed. TODO: FIX COMMENT. (Contributed by NM, 6-May-2013.) (New usage is discouraged.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg16z 35947	Eliminate $.\/$ $.\/$ condition from cdlemg16 35945. TODO: would it help to also eliminate here or later? (Contributed by NM, 25-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg16zz 35948	Eliminate from cdlemg16z 35947. TODO: Use this only if needed. (Contributed by NM, 26-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg17a 35949	TODO: FIX COMMENT. (Contributed by NM, 8-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17b 35950*	Part of proof of Lemma G in [Crawley] p. 117, 4th line. Whenever (in their terminology) p $\/$ q/0 (i.e. the sublattice from 0 to p $\/$ q) contains precisely three atoms and g is not the identity, g(p) = q. See also comments under cdleme0nex 35577. (Contributed by NM, 8-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17dN 35951*	TODO: fix comment. (Contributed by NM, 9-May-2013.) (New usage is discouraged.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$ $./\$

Theorem	cdlemg17dALTN 35952	Same as cdlemg17dN 35951 with fewer antecedents but longer proof TODO: fix comment. (Contributed by NM, 9-May-2013.) (New usage is discouraged.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $./\$

Theorem	cdlemg17e 35953*	TODO: fix comment. (Contributed by NM, 8-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $.\/$

Theorem	cdlemg17f 35954*	TODO: fix comment. (Contributed by NM, 8-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $.\/$

Theorem	cdlemg17g 35955*	TODO: fix comment. (Contributed by NM, 9-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$

Theorem	cdlemg17h 35956*	TODO: fix comment. (Contributed by NM, 10-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $\/$

Theorem	cdlemg17i 35957*	TODO: fix comment. (Contributed by NM, 10-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17ir 35958*	TODO: fix comment. (Contributed by NM, 13-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17j 35959*	TODO: fix comment. (Contributed by NM, 11-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17pq 35960*	Utility theorem for swapping and . TODO: fix comment. (Contributed by NM, 11-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17bq 35961*	cdlemg17b 35950 with and swapped. Antecedent is redundant for easier use. TODO: should we have redundant antecedent for cdlemg17b 35950 also? (Contributed by NM, 13-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17iqN 35962*	cdlemg17i 35957 with and swapped. (Contributed by NM, 13-May-2013.) (New usage is discouraged.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $/\$

Theorem	cdlemg17irq 35963*	cdlemg17ir 35958 with and swapped. (Contributed by NM, 13-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17jq 35964*	cdlemg17j 35959 with and swapped. (Contributed by NM, 13-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$

Theorem	cdlemg17 35965*	Part of Lemma G of [Crawley] p. 117, lines 7 and 8. We show an argument whose value at equals itself. TODO: fix comment. (Contributed by NM, 12-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemg18a 35966	Show two lines are different. TODO: fix comment. (Contributed by NM, 14-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $.\/$

Theorem	cdlemg18b 35967	Lemma for cdlemg18c 35968. TODO: fix comment. (Contributed by NM, 15-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$

Theorem	cdlemg18c 35968	Show two lines intersect at an atom. TODO: fix comment. (Contributed by NM, 15-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemg18d 35969*	Show two lines intersect at an atom. TODO: fix comment. (Contributed by NM, 15-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemg18 35970*	Show two lines intersect at an atom. TODO: fix comment. (Contributed by NM, 15-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$

Theorem	cdlemg19a 35971*	Show two lines intersect at an atom. TODO: fix comment. (Contributed by NM, 15-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $.\/$ $./\$

Theorem	cdlemg19 35972*	Show two lines intersect at an atom. TODO: fix comment. (Contributed by NM, 15-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg20 35973*	Show two lines intersect at an atom. TODO: fix comment. (Contributed by NM, 23-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg21 35974*	Version of cdlemg19 with $.\/$ instead of $.\/$ as a condition. (Contributed by NM, 23-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg22 35975*	cdlemg21 35974 with condition removed. (Contributed by NM, 23-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg24 35976*	Combine cdlemg16z 35947 and cdlemg22 35975. TODO: Fix comment. (Contributed by NM, 24-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg37 35977*	Use cdlemg8 35919 to eliminate the $.\/$ condition of cdlemg24 35976. (Contributed by NM, 31-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg25zz 35978	cdlemg16zz 35948 restated for easier studying. TODO: Discard this after everything is figured out. (Contributed by NM, 26-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg26zz 35979	cdlemg16zz 35948 restated for easier studying. TODO: Discard this after everything is figured out. (Contributed by NM, 26-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg27a 35980	For use with case when $.\/$ $./\$ $.\/$ or $.\/$ $./\$ $.\/$ is zero, letting us establish $/\$ $.\/$ via 4atex 35362. TODO: Fix comment. (Contributed by NM, 28-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$

Theorem	cdlemg28a 35981	Part of proof of Lemma G of [Crawley] p. 116. First equality of the equation of line 14 on p. 117. (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg31b0N 35982	TODO: Fix comment. (Contributed by NM, 30-May-2013.) (New usage is discouraged.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $\/$

Theorem	cdlemg31b0a 35983	TODO: Fix comment. (Contributed by NM, 30-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $\/$

Theorem	cdlemg27b 35984	TODO: Fix comment. (Contributed by NM, 28-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $.\/$

Theorem	cdlemg31a 35985	TODO: fix comment. (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg31b 35986	TODO: fix comment. (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg31c 35987	Show that when is an atom, it is not under . TODO: Is there a shorter direct proof? TODO: should we eliminate here? (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg31d 35988	Eliminate from cdlemg31c 35987. TODO: Prove directly. TODO: do we need to eliminate ? It might be better to do this all at once at the end. See also cdlemg29 35993 vs. cdlemg28 35992. (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$

Theorem	cdlemg33b0 35989*	TODO: Fix comment. (Contributed by NM, 30-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $.\/$

Theorem	cdlemg33c0 35990*	TODO: Fix comment. (Contributed by NM, 30-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $.\/$

Theorem	cdlemg28b 35991*	Part of proof of Lemma G of [Crawley] p. 116. Second equality of the equation of line 14 on p. 117. Note that is redundant here (but simplifies cdlemg28 35992.) (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg28 35992*	Part of proof of Lemma G of [Crawley] p. 116. Chain the equalities of line 14 on p. 117. TODO: rearrange hypotheses in the order of cdlemg29 35993 (and maybe leading up to this too)? (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg29 35993*	Eliminate and from cdlemg28 35992. TODO: would it be better to do this later? (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $/\$ $/\$ $.\/$ $./\$ $.\/$ $./\$

Theorem	cdlemg33a 35994*	TODO: Fix comment. (Contributed by NM, 29-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg33b 35995*	TODO: Fix comment. (Contributed by NM, 30-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg33c 35996*	TODO: Fix comment. (Contributed by NM, 30-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg33d 35997*	TODO: Fix comment. (Contributed by NM, 30-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg33e 35998*	TODO: Fix comment. (Contributed by NM, 30-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg33 35999*	Combine cdlemg33b 35995, cdlemg33c 35996, cdlemg33d 35997, cdlemg33e 35998. TODO: Fix comment. (Contributed by NM, 30-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $/\$ $/\$ $/\$ $.\/$

Theorem	cdlemg34 36000*	Use cdlemg33 to eliminate from cdlemg29 35993. TODO: Fix comment. (Contributed by NM, 31-May-2013.)
$.\/$ $./\$ $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $/\$ $.\/$ $.\/$ $.\/$ $./\$ $.\/$ $./\$

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