Nuprl Lemma : is-dag-add
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[y:ℕlg-size(g)]. ∀[x:ℕy]. 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
Lemmas :
lg-size-add,
lg-edge-add,
lelt_wf,
lg-edge_wf,
lg-add_wf,
less_than_transitivity2,
le_weakening2,
int_seg_wf,
lg-size_wf,
member-less_than,
nat_wf,
is-dag_wf,
labeled-graph_wf
Latex:
\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:
2015_07_22-PM-00_29_51
Last ObjectModification:
2015_01_28-PM-11_33_18
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