{ 
[T:Type]. [g:LabeledGraph(T)]. [y:
lg-size(g)]. [x:y].
is-dag(lg-add(g;x;y)) supposing is-dag(g) }
{ Proof }
Definitions occuring in Statement :
is-dag: is-dag(g),
lg-add: lg-add(g;a;b),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j
},
uimplies: b supposing a,
uall: [x:A]. B[x],
natural_number: $n,
universe: Type
Definitions :
uall: [x:A]. B[x],
int_seg: {i..j},
uimplies: b supposing a,
is-dag: is-dag(g),
member: t 
T,
all: x:A. B[x],
implies: P 
Q,
lelt: i 
j < k,
and: P 
Q,
or: P 
Q,
iff: P 
Q,
le: A B,
not: 
A,
false: False,
prop: 
,
nat: ,
guard: {T}
Lemmas :
lg-size-add,
lg-edge-add,
le_wf,
lg-edge_wf,
lg-add_wf,
int_seg_wf,
lg-size_wf,
nat_wf,
is-dag_wf,
labeled-graph_wf
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[y:\mBbbN{}lg-size(g)]. \mforall{}[x:\mBbbN{}y].
is-dag(lg-add(g;x;y)) supposing is-dag(g)
Date html generated:
2011_08_16-PM-06_42_52
Last ObjectModification:
2011_06_20-AM-02_01_51
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