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Share distinct variable conditions
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BTernaryTau committed Oct 12, 2023
1 parent 6849380 commit 6f737d7
Showing 1 changed file with 1 addition and 7 deletions.
8 changes: 1 addition & 7 deletions set.mm
Original file line number Diff line number Diff line change
Expand Up @@ -501800,16 +501800,13 @@ have become an indirect lemma of the theorem in question (i.e. a lemma
cacycgr $a class AcyclicGraph $.

${
$d g f p $.
$d f g p $.
$( Define the class of all acyclic graphs. A graph is called _acyclic_ if
it has no (non-trivial) cycles. (Contributed by BTernaryTau,
11-Oct-2023.) $)
df-acycgr $a |- AcyclicGraph =
{ g | -. E. f E. p ( f ( Cycles ` g ) p /\ f =/= (/) ) } $.
$}

${
$d f g p $.
$( An alternate definition of the class of all acyclic graphs that requires
all cycles to be trivial. (Contributed by BTernaryTau, 11-Oct-2023.) $)
dfacycgr1 $p |- AcyclicGraph =
Expand All @@ -501829,10 +501826,7 @@ it has no (non-trivial) cycles. (Contributed by BTernaryTau,
( vg cv ccycls cfv wbr c0 wne wa wex wn cacycgr wceq fveq2 anbi1d 2exbidv
breqd notbid df-acycgr elab2g ) AFZDFZEFZGHZIZUDJKZLZDMAMZNUDUEBGHZIZUILZ
DMAMZNEBOCUFBPZUKUOUPUJUNADUPUHUMUIUPUGULUDUEUFBGQTRSUAAEDUBUC $.
$}

${
$d f g G p $.
$( The property of being an acyclic graph. (Contributed by BTernaryTau,
11-Oct-2023.) $)
isacycgr1 $p |- ( G e. W -> ( G e. AcyclicGraph <->
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