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Theorem cdlemg42 30168
Description: Part of proof of Lemma G of [Crawley] p. 116, first line of third paragraph on p. 117. (Contributed by NM, 3-Jun-2013.)
Hypotheses
Ref Expression
cdlemg42.l  |-  .<_  =  ( le `  K )
cdlemg42.j  |-  .\/  =  ( join `  K )
cdlemg42.a  |-  A  =  ( Atoms `  K )
cdlemg42.h  |-  H  =  ( LHyp `  K
)
cdlemg42.t  |-  T  =  ( ( LTrn `  K
) `  W )
cdlemg42.r  |-  R  =  ( ( trL `  K
) `  W )
Assertion
Ref Expression
cdlemg42  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  -.  ( G `  P )  .<_  ( P  .\/  ( F `  P )
) )

Proof of Theorem cdlemg42
StepHypRef Expression
1 simp33 998 . 2  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  ( R `  F )  =/=  ( R `  G )
)
2 simpl1l 1011 . . . . . . . . 9  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  K  e.  HL )
3 simp31l 1083 . . . . . . . . . 10  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  P  e.  A )
43adantr 453 . . . . . . . . 9  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  P  e.  A )
5 simp1 960 . . . . . . . . . . 11  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  ( K  e.  HL  /\  W  e.  H ) )
6 simp2l 986 . . . . . . . . . . 11  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  F  e.  T )
7 cdlemg42.l . . . . . . . . . . . 12  |-  .<_  =  ( le `  K )
8 cdlemg42.a . . . . . . . . . . . 12  |-  A  =  ( Atoms `  K )
9 cdlemg42.h . . . . . . . . . . . 12  |-  H  =  ( LHyp `  K
)
10 cdlemg42.t . . . . . . . . . . . 12  |-  T  =  ( ( LTrn `  K
) `  W )
117, 8, 9, 10ltrnat 29579 . . . . . . . . . . 11  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  F  e.  T  /\  P  e.  A
)  ->  ( F `  P )  e.  A
)
125, 6, 3, 11syl3anc 1187 . . . . . . . . . 10  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  ( F `  P )  e.  A
)
1312adantr 453 . . . . . . . . 9  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( F `  P )  e.  A )
14 cdlemg42.j . . . . . . . . . 10  |-  .\/  =  ( join `  K )
157, 14, 8hlatlej1 28814 . . . . . . . . 9  |-  ( ( K  e.  HL  /\  P  e.  A  /\  ( F `  P )  e.  A )  ->  P  .<_  ( P  .\/  ( F `  P ) ) )
162, 4, 13, 15syl3anc 1187 . . . . . . . 8  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  P  .<_  ( P  .\/  ( F `  P )
) )
17 simpr 449 . . . . . . . 8  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( G `  P )  .<_  ( P  .\/  ( F `  P )
) )
18 hllat 28803 . . . . . . . . . 10  |-  ( K  e.  HL  ->  K  e.  Lat )
192, 18syl 17 . . . . . . . . 9  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  K  e.  Lat )
20 eqid 2258 . . . . . . . . . . 11  |-  ( Base `  K )  =  (
Base `  K )
2120, 8atbase 28729 . . . . . . . . . 10  |-  ( P  e.  A  ->  P  e.  ( Base `  K
) )
224, 21syl 17 . . . . . . . . 9  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  P  e.  ( Base `  K
) )
23 simp2r 987 . . . . . . . . . . . 12  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  G  e.  T )
247, 8, 9, 10ltrnat 29579 . . . . . . . . . . . 12  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  G  e.  T  /\  P  e.  A
)  ->  ( G `  P )  e.  A
)
255, 23, 3, 24syl3anc 1187 . . . . . . . . . . 11  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  ( G `  P )  e.  A
)
2625adantr 453 . . . . . . . . . 10  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( G `  P )  e.  A )
2720, 8atbase 28729 . . . . . . . . . 10  |-  ( ( G `  P )  e.  A  ->  ( G `  P )  e.  ( Base `  K
) )
2826, 27syl 17 . . . . . . . . 9  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( G `  P )  e.  ( Base `  K
) )
2920, 14, 8hlatjcl 28806 . . . . . . . . . 10  |-  ( ( K  e.  HL  /\  P  e.  A  /\  ( F `  P )  e.  A )  -> 
( P  .\/  ( F `  P )
)  e.  ( Base `  K ) )
302, 4, 13, 29syl3anc 1187 . . . . . . . . 9  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( P  .\/  ( F `  P ) )  e.  ( Base `  K
) )
3120, 7, 14latjle12 14131 . . . . . . . . 9  |-  ( ( K  e.  Lat  /\  ( P  e.  ( Base `  K )  /\  ( G `  P )  e.  ( Base `  K
)  /\  ( P  .\/  ( F `  P
) )  e.  (
Base `  K )
) )  ->  (
( P  .<_  ( P 
.\/  ( F `  P ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  <->  ( P  .\/  ( G `  P
) )  .<_  ( P 
.\/  ( F `  P ) ) ) )
3219, 22, 28, 30, 31syl13anc 1189 . . . . . . . 8  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  (
( P  .<_  ( P 
.\/  ( F `  P ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  <->  ( P  .\/  ( G `  P
) )  .<_  ( P 
.\/  ( F `  P ) ) ) )
3316, 17, 32mpbi2and 892 . . . . . . 7  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( P  .\/  ( G `  P ) )  .<_  ( P  .\/  ( F `
 P ) ) )
34 simpl32 1042 . . . . . . . . 9  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( G `  P )  =/=  P )
3534necomd 2504 . . . . . . . 8  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  P  =/=  ( G `  P
) )
367, 14, 8ps-1 28916 . . . . . . . 8  |-  ( ( K  e.  HL  /\  ( P  e.  A  /\  ( G `  P
)  e.  A  /\  P  =/=  ( G `  P ) )  /\  ( P  e.  A  /\  ( F `  P
)  e.  A ) )  ->  ( ( P  .\/  ( G `  P ) )  .<_  ( P  .\/  ( F `
 P ) )  <-> 
( P  .\/  ( G `  P )
)  =  ( P 
.\/  ( F `  P ) ) ) )
372, 4, 26, 35, 4, 13, 36syl132anc 1205 . . . . . . 7  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  (
( P  .\/  ( G `  P )
)  .<_  ( P  .\/  ( F `  P ) )  <->  ( P  .\/  ( G `  P ) )  =  ( P 
.\/  ( F `  P ) ) ) )
3833, 37mpbid 203 . . . . . 6  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( P  .\/  ( G `  P ) )  =  ( P  .\/  ( F `  P )
) )
3938oveq1d 5807 . . . . 5  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  (
( P  .\/  ( G `  P )
) ( meet `  K
) W )  =  ( ( P  .\/  ( F `  P ) ) ( meet `  K
) W ) )
40 simpl1 963 . . . . . 6  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( K  e.  HL  /\  W  e.  H ) )
41 simpl2r 1014 . . . . . 6  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  G  e.  T )
42 simpl31 1041 . . . . . 6  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( P  e.  A  /\  -.  P  .<_  W ) )
43 eqid 2258 . . . . . . 7  |-  ( meet `  K )  =  (
meet `  K )
44 cdlemg42.r . . . . . . 7  |-  R  =  ( ( trL `  K
) `  W )
457, 14, 43, 8, 9, 10, 44trlval2 29602 . . . . . 6  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  G  e.  T  /\  ( P  e.  A  /\  -.  P  .<_  W ) )  ->  ( R `  G )  =  ( ( P  .\/  ( G `  P )
) ( meet `  K
) W ) )
4640, 41, 42, 45syl3anc 1187 . . . . 5  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( R `  G )  =  ( ( P 
.\/  ( G `  P ) ) (
meet `  K ) W ) )
47 simpl2l 1013 . . . . . 6  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  F  e.  T )
487, 14, 43, 8, 9, 10, 44trlval2 29602 . . . . . 6  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  F  e.  T  /\  ( P  e.  A  /\  -.  P  .<_  W ) )  ->  ( R `  F )  =  ( ( P  .\/  ( F `  P )
) ( meet `  K
) W ) )
4940, 47, 42, 48syl3anc 1187 . . . . 5  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( R `  F )  =  ( ( P 
.\/  ( F `  P ) ) (
meet `  K ) W ) )
5039, 46, 493eqtr4rd 2301 . . . 4  |-  ( ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  ( ( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `
 F )  =/=  ( R `  G
) ) )  /\  ( G `  P ) 
.<_  ( P  .\/  ( F `  P )
) )  ->  ( R `  F )  =  ( R `  G ) )
5150ex 425 . . 3  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  ( ( G `  P )  .<_  ( P  .\/  ( F `  P )
)  ->  ( R `  F )  =  ( R `  G ) ) )
5251necon3ad 2457 . 2  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  ( ( R `  F )  =/=  ( R `  G
)  ->  -.  ( G `  P )  .<_  ( P  .\/  ( F `  P )
) ) )
531, 52mpd 16 1  |-  ( ( ( K  e.  HL  /\  W  e.  H )  /\  ( F  e.  T  /\  G  e.  T )  /\  (
( P  e.  A  /\  -.  P  .<_  W )  /\  ( G `  P )  =/=  P  /\  ( R `  F
)  =/=  ( R `
 G ) ) )  ->  -.  ( G `  P )  .<_  ( P  .\/  ( F `  P )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    <-> wb 178    /\ wa 360    /\ w3a 939    = wceq 1619    e. wcel 1621    =/= wne 2421   class class class wbr 3997   ` cfv 4673  (class class class)co 5792   Basecbs 13111   lecple 13178   joincjn 14041   meetcmee 14042   Latclat 14114   Atomscatm 28703   HLchlt 28790   LHypclh 29423   LTrncltrn 29540   trLctrl 29597
This theorem is referenced by:  cdlemg43  30169
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-13 1625  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239  ax-rep 4105  ax-sep 4115  ax-nul 4123  ax-pow 4160  ax-pr 4186  ax-un 4484
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2122  df-mo 2123  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ne 2423  df-nel 2424  df-ral 2523  df-rex 2524  df-reu 2525  df-rab 2527  df-v 2765  df-sbc 2967  df-csb 3057  df-dif 3130  df-un 3132  df-in 3134  df-ss 3141  df-nul 3431  df-if 3540  df-pw 3601  df-sn 3620  df-pr 3621  df-op 3623  df-uni 3802  df-iun 3881  df-br 3998  df-opab 4052  df-mpt 4053  df-id 4281  df-xp 4675  df-rel 4676  df-cnv 4677  df-co 4678  df-dm 4679  df-rn 4680  df-res 4681  df-ima 4682  df-fun 4683  df-fn 4684  df-f 4685  df-f1 4686  df-fo 4687  df-f1o 4688  df-fv 4689  df-ov 5795  df-oprab 5796  df-mpt2 5797  df-1st 6056  df-2nd 6057  df-iota 6225  df-undef 6264  df-riota 6272  df-map 6742  df-poset 14043  df-plt 14055  df-lub 14071  df-glb 14072  df-join 14073  df-p0 14108  df-lat 14115  df-oposet 28616  df-ol 28618  df-oml 28619  df-covers 28706  df-ats 28707  df-atl 28738  df-cvlat 28762  df-hlat 28791  df-lhyp 29427  df-laut 29428  df-ldil 29543  df-ltrn 29544  df-trl 29598
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