Type  Label  Description 
Statement 

Theorem  sucidALTVD 36701 
A set belongs to its successor. Alternate proof of sucid 5489.
The following User's Proof is a Virtual Deduction proof
completed automatically by the tools program
completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm
Megill's Metamath Proof Assistant. sucidALT 36702 is sucidALTVD 36701
without virtual deductions and was automatically derived from
sucidALTVD 36701. This proof illustrates that
completeusersproof.cmd will generate a Metamath proof from any
User's Proof which is "conventional" in the sense that no step
is a virtual deduction, provided that all necessary unification
theorems and transformation deductions are in set.mm.
completeusersproof.cmd automatically converts such a
conventional proof into a Virtual Deduction proof for which each
step happens to be a 0virtual hypothesis virtual deduction.
The user does not need to search for reference theorem labels or
deduction labels nor does he(she) need to use theorems and
deductions which unify with reference theorems and deductions in
set.mm. All that is necessary is that each theorem or deduction
of the User's Proof unifies with some reference theorem or
deduction in set.mm or is a semantic variation of some theorem
or deduction which unifies with some reference theorem or
deduction in set.mm. The definition of "semantic variation" has
not been precisely defined. If it is obvious that a theorem or
deduction has the same meaning as another theorem or deduction,
then it is a semantic variation of the latter theorem or
deduction. For example, step 4 of the User's Proof is a
semantic variation of the definition (axiom)
, which unifies with dfsuc 5416, a
reference definition (axiom) in set.mm. Also, a theorem or
deduction is said to be a semantic variation of another
theorem or deduction if it is obvious upon cursory inspection
that it has the same meaning as a weaker form of the latter
theorem or deduction. For example, the deduction
infers is a
semantic variation of the theorem
, which unifies with
the set.mm reference definition (axiom) dford2 8070.
h1:: 
 2:1: 
 3:2: 
 4:: 
 qed:3,4: 

(Contributed by Alan Sare, 18Feb2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sucidALT 36702 
A set belongs to its successor. This proof was automatically derived
from sucidALTVD 36701 using translate_{without}_overwriting.cmd and
minimizing. (Contributed by Alan Sare, 18Feb2012.)
(Proof modification is discouraged.) (New usage is discouraged.)



Theorem  sucidVD 36703 
A set belongs to its successor. The following User's Proof is a
Virtual Deduction proof completed automatically by the tools
program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2
and Norm Megill's Metamath Proof Assistant.
sucid 5489 is sucidVD 36703 without virtual deductions and was automatically
derived from sucidVD 36703.
h1:: 
 2:1: 
 3:2: 
 4:: 
 qed:3,4: 

(Contributed by Alan Sare, 18Feb2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  imbi12VD 36704 
Implication form of imbi12i 324.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
imbi12 320 is imbi12VD 36704 without virtual deductions and was automatically
derived from imbi12VD 36704.
1:: 
 2:: 
 3:: 
 4:1,3: 
 5:2,4: 
 6:5: 
 7:: 
 8:1,7: 
 9:2,8: 
 10:9: 
 11:6,10: 
 12:11: 
 qed:12: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  imbi13VD 36705 
Join three logical equivalences to form equivalence of implications.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
imbi13 36307 is imbi13VD 36705 without virtual deductions and was automatically
derived from imbi13VD 36705.
1:: 
 2:: 
 3:: 
 4:2,3: 
 5:1,4: 
 6:5: 
 7:6: 
 qed:7: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sbcim2gVD 36706 
Distribution of class substitution over a leftnested implication.
Similar to sbcimg 3319.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
sbcim2g 36329 is sbcim2gVD 36706 without virtual deductions and was automatically
derived from sbcim2gVD 36706.
1:: 
 2:: 
 3:1,2: 
 4:1: 
 5:3,4: 
 6:5: 
 7:: 
 8:4,7: 
 9:1: 
 10:8,9: 
 11:10: 
 12:6,11: 
 qed:12: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sbcbiVD 36707 
Implication form of sbcbiiOLD 36322.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
sbcbi 36330 is sbcbiVD 36707 without virtual deductions and was automatically
derived from sbcbiVD 36707.
1:: 
 2:: 
 3:1,2: 
 4:1,3: 
 5:4: 
 qed:5: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  trsbcVD 36708* 
Formulabuilding inference rule for class substitution, substituting a
class variable for the setvar variable of the transitivity predicate.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
trsbc 36331 is trsbcVD 36708 without virtual deductions and was automatically
derived from trsbcVD 36708.
1:: 
 2:1: 
 3:1: 
 4:1: 
 5:1,2,3,4: 
 6:1: 
 7:5,6: 
 8:: 
 9:7,8: 
 10:: 
 11:10: 
 12:1,11: 
 13:9,12: 
 14:13: 
 15:14: 
 16:1: 
 17:15,16: 
 18:17: 
 19:18: 
 20:1: 
 21:19,20: 
 22:: 
 23:21,22: 
 24:: 
 25:24: 
 26:1,25: 
 27:23,26: 
 qed:27: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  truniALTVD 36709* 
The union of a class of transitive sets is transitive.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
truniALT 36332 is truniALTVD 36709 without virtual deductions and was
automatically derived from truniALTVD 36709.
1:: 
 2:: 
 3:2: 
 4:2: 
 5:4: 
 6:: 
 7:6: 
 8:6: 
 9:1,8: 
 10:8,9: 
 11:3,7,10: 
 12:11,8: 
 13:12: 
 14:13: 
 15:14: 
 16:5,15: 
 17:16: 
 18:17: 
 19:18: 
 qed:19: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  ee33VD 36710 
Nonvirtual deduction form of e33 36555.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
ee33 36308 is ee33VD 36710 without virtual deductions and was automatically
derived from ee33VD 36710.
h1:: 
 h2:: 
 h3:: 
 4:1,3: 
 5:4: 
 6:2,5: 
 7:6: 
 8:7: 
 qed:8: 

(Contributed by Alan Sare, 18Mar2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  trintALTVD 36711* 
The intersection of a class of transitive sets is transitive. Virtual
deduction proof of trintALT 36712.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
trintALT 36712 is trintALTVD 36711 without virtual deductions and was
automatically derived from trintALTVD 36711.
1:: 
 2:: 
 3:2: 
 4:2: 
 5:4: 
 6:5: 
 7:: 
 8:7,6: 
 9:7,1: 
 10:7,9: 
 11:10,3,8: 
 12:11: 
 13:12: 
 14:13: 
 15:3,14: 
 16:15: 
 17:16: 
 18:17: 
 qed:18: 

(Contributed by Alan Sare, 17Apr2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  trintALT 36712* 
The intersection of a class of transitive sets is transitive. Exercise
5(b) of [Enderton] p. 73. trintALT 36712 is an alternative proof of
trint 4504. trintALT 36712 is trintALTVD 36711 without virtual deductions and was
automatically derived from trintALTVD 36711 using the tools program
translate..without..overwriting.cmd and Metamath's minimize command.
(Contributed by Alan Sare, 17Apr2012.)
(Proof modification is discouraged.) (New usage is discouraged.)



Theorem  undif3VD 36713 
The first equality of Exercise 13 of [TakeutiZaring] p. 22. Virtual
deduction proof of undif3 3711.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
undif3 3711 is undif3VD 36713 without virtual deductions and was automatically
derived from undif3VD 36713.
1:: 
 2:: 
 3:2: 
 4:1,3: 
 5:: 
 6:5: 
 7:5: 
 8:6,7: 
 9:8: 
 10:: 
 11:10: 
 12:10: 
 13:11: 
 14:12: 
 15:13,14: 
 16:15: 
 17:9,16: 
 18:: 
 19:18: 
 20:18: 
 21:18: 
 22:21: 
 23:: 
 24:23: 
 25:24: 
 26:25: 
 27:10: 
 28:27: 
 29:: 
 30:29: 
 31:30: 
 32:31: 
 33:22,26: 
 34:28,32: 
 35:33,34: 
 36:: 
 37:36,35: 
 38:17,37: 
 39:: 
 40:39: 
 41:: 
 42:40,41: 
 43:: 
 44:43,42: 
 45:: 
 46:45,44: 
 47:4,38: 
 48:46,47: 
 49:48: 
 qed:49: 

(Contributed by Alan Sare, 17Apr2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  sbcssgVD 36714 
Virtual deduction proof of sbcssg 3884.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
sbcssg 3884 is sbcssgVD 36714 without virtual deductions and was automatically
derived from sbcssgVD 36714.
1:: 
 2:1: 
 3:1: 
 4:2,3: 
 5:1: 
 6:4,5: 
 7:6: 
 8:7: 
 9:1: 
 10:8,9: 
 11:: 
 110:11: 
 12:1,110: 
 13:10,12: 
 14:: 
 15:13,14: 
 qed:15: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbingVD 36715 
Virtual deduction proof of csbingOLD 36649.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
csbingOLD 36649 is csbingVD 36715 without virtual deductions and was
automatically derived from csbingVD 36715.
1:: 
 2:: 
 20:2: 
 30:1,20: 
 3:1,30: 
 4:1: 
 5:3,4: 
 6:1: 
 7:1: 
 8:6,7: 
 9:1: 
 10:9,8: 
 11:10: 
 12:11: 
 13:5,12: 
 14:: 
 15:13,14: 
 qed:15: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem5VD 36716* 
Virtual deduction proof of onfrALTlem5 36338.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
onfrALTlem5 36338 is onfrALTlem5VD 36716 without virtual deductions and was
automatically derived from onfrALTlem5VD 36716.
1:: 
 2:1: 
 3:2: 
 4:3: 
 5:: 
 6:4,5: 
 7:2: 
 8:: 
 9:8: 
 10:2,9: 
 11:7,10: 
 12:6,11: 
 13:2: 
 14:12,13: 
 15:2: 
 16:15,14: 
 17:2: 
 18:2: 
 19:2: 
 20:18,19: 
 21:17,20: 
 22:2: 
 23:2: 
 24:21,23: 
 25:22,24: 
 26:2: 
 27:25,26: 
 28:2: 
 29:27,28: 
 30:29: 
 31:30: 
 32:: 
 33:31,32: 
 34:2: 
 35:33,34: 
 36:: 
 37:36: 
 38:2,37: 
 39:35,38: 
 40:16,39: 
 41:2: 
 qed:40,41: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem4VD 36717* 
Virtual deduction proof of onfrALTlem4 36339.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
onfrALTlem4 36339 is onfrALTlem4VD 36717 without virtual deductions and was
automatically derived from onfrALTlem4VD 36717.
1:: 
 2:1: 
 3:1: 
 4:1: 
 5:1: 
 6:4,5: 
 7:3,6: 
 8:1: 
 9:7,8: 
 10:2,9: 
 11:1: 
 12:11,10: 
 13:1: 
 qed:13,12: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem3VD 36718* 
Virtual deduction proof of onfrALTlem3 36340.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
onfrALTlem3 36340 is onfrALTlem3VD 36718 without virtual deductions and was
automatically derived from onfrALTlem3VD 36718.
1:: 
 2:: 
 3:2: 
 4:1: 
 5:3,4: 
 6:5: 
 7:6: 
 8:: 
 9:7,8: 
 10:9: 
 11:10: 
 12:: 
 13:12,8: 
 14:13,11: 
 15:: 
 16:14,15: 
 17:: 
 18:2: 
 19:18: 
 20:17,19: 
 qed:16,20: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  simplbi2comtVD 36719 
Virtual deduction proof of simplbi2comt 624.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
simplbi2comt 624 is simplbi2comtVD 36719 without virtual deductions and was
automatically derived from simplbi2comtVD 36719.
1:: 
 2:1: 
 3:2: 
 4:3: 
 qed:4: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem2VD 36720* 
Virtual deduction proof of onfrALTlem2 36342.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
onfrALTlem2 36342 is onfrALTlem2VD 36720 without virtual deductions and was
automatically derived from onfrALTlem2VD 36720.
1:: 
 2:1: 
 3:2: 
 4:: 
 5:: 
 6:5: 
 7:4: 
 8:6,7: 
 9:8: 
 10:9: 
 11:1: 
 12:11: 
 13:2: 
 14:10,12,13: 
 15:3,14: 
 16:13,15: 
 17:16: 
 18:17: 
 19:18: 
 20:: 
 21:20: 
 22:19,21: 
 23:20: 
 24:23: 
 25:22,24: 
 26:25: 
 27:26: 
 28:27: 
 29:: 
 30:29: 
 31:28,30: 
 qed:31: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTlem1VD 36721* 
Virtual deduction proof of onfrALTlem1 36344.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
onfrALTlem1 36344 is onfrALTlem1VD 36721 without virtual deductions and was
automatically derived from onfrALTlem1VD 36721.
1:: 
 2:1: 
 3:2: 
 4:: 
 5:4: 
 6:5: 
 7:3,6: 
 8:: 
 qed:7,8: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  onfrALTVD 36722 
Virtual deduction proof of onfrALT 36345.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
onfrALT 36345 is onfrALTVD 36722 without virtual deductions and was
automatically derived from onfrALTVD 36722.
1:: 
 2:: 
 3:1: 
 4:2: 
 5:: 
 6:5,4,3: 
 7:6: 
 8:7: 
 9:8: 
 10:: 
 11:9,10: 
 12:: 
 13:12: 
 14:13,11: 
 15:14: 
 16:15: 
 qed:16: 

(Contributed by Alan Sare, 22Jul2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbeq2gVD 36723 
Virtual deduction proof of csbeq2gOLD 36346.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
csbeq2gOLD 36346 is csbeq2gVD 36723 without virtual deductions and was
automatically derived from csbeq2gVD 36723.
1:: 
 2:1: 
 3:1: 
 4:2,3: 
 qed:4: 

(Contributed by Alan Sare, 10Nov2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbsngVD 36724 
Virtual deduction proof of csbsng 4030.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
csbsng 4030 is csbsngVD 36724 without virtual deductions and was automatically
derived from csbsngVD 36724.
1:: 
 2:1: 
 3:1: 
 4:3: 
 5:2,4: 
 6:5: 
 7:6: 
 8:1: 
 9:7,8: 
 10:: 
 11:10: 
 12:1,11: 
 13:9,12: 
 14:: 
 15:13,14: 
 qed:15: 

(Contributed by Alan Sare, 10Nov2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbxpgVD 36725 
Virtual deduction proof of csbxpgOLD 36648.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
csbxpgOLD 36648 is csbxpgVD 36725 without virtual deductions and was
automatically derived from csbxpgVD 36725.
1:: 
 2:1: 
 3:1: 
 4:3: 
 5:2,4: 
 6:1: 
 7:1: 
 8:7: 
 9:6,8: 
 10:5,9: 
 11:1: 
 12:10,11: 
 13:1: 
 14:12,13: 
 15:1: 
 16:14,15: 
 17:16: 
 18:17: 
 19:1: 
 20:18,19: 
 21:20: 
 22:21: 
 23:1: 
 24:22,23: 
 25:24: 
 26:25: 
 27:1: 
 28:26,27: 
 29:: 
 30:: 
 31:29,30: 
 32:31: 
 33:1,32: 
 34:28,33: 
 35:: 
 36:: 
 37:35,36: 
 38:34,37: 
 qed:38: 

(Contributed by Alan Sare, 10Nov2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbresgVD 36726 
Virtual deduction proof of csbresgOLD 36650.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
csbresgOLD 36650 is csbresgVD 36726 without virtual deductions and was
automatically derived from csbresgVD 36726.
1:: 
 2:1: 
 3:2: 
 4:1: 
 5:3,4: 
 6:5: 
 7:1: 
 8:6,7: 
 9:: 
 10:9: 
 11:1,10: 
 12:8,11: 
 13:: 
 14:12,13: 
 qed:14: 

(Contributed by Alan Sare, 10Nov2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbrngVD 36727 
Virtual deduction proof of csbrngOLD 36651.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
csbrngOLD 36651 is csbrngVD 36727 without virtual deductions and was
automatically derived from csbrngVD 36727.
1:: 
 2:1: 
 3:1: 
 4:3: 
 5:2,4: 
 6:5: 
 7:6: 
 8:1: 
 9:7,8: 
 10:9: 
 11:10: 
 12:1: 
 13:11,12: 
 14:: 
 15:14: 
 16:1,15: 
 17:13,16: 
 18:: 
 19:17,18: 
 qed:19: 

(Contributed by Alan Sare, 10Nov2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbima12gALTVD 36728 
Virtual deduction proof of csbima12gALTOLD 36652.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
csbima12gALTOLD 36652 is csbima12gALTVD 36728 without virtual deductions and was
automatically derived from csbima12gALTVD 36728.
1:: 
 2:1: 
 3:2: 
 4:1: 
 5:3,4: 
 6:: 
 7:6: 
 8:1,7: 
 9:5,8: 
 10:: 
 11:9,10: 
 qed:11: 

(Contributed by Alan Sare, 10Nov2012.) (Proof modification is
discouraged.) (New usage is discouraged.)



Theorem  csbunigVD 36729 
Virtual deduction proof of csbunigOLD 36646.
The following User's Proof is a Virtual Deduction proof completed
automatically by the tools program completeusersproof.cmd, which invokes
Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant.
csbunigOLD 36646 is csbunigVD 36729 without virtual deductions and was
automatically derived from csbunigVD 36729.
1:: 
 2:1: 
 3:1: 
 4:2,3: 
 5:1: 
 6:4,5: 
 