Nuprl Lemma : is-dag-map
∀[T,S:Type]. ∀[f:T ─→ S]. ∀[g:LabeledGraph(T)]. is-dag(lg-map(f;g)) supposing is-dag(g)
Proof
Definitions occuring in Statement :
lg-map: lg-map(f;g),
is-dag: is-dag(g),
labeled-graph: LabeledGraph(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
lg-size-map,
less_than_transitivity1,
lg-size_wf,
lg-map_wf,
nat_wf,
le_weakening,
lelt_wf,
lg-edge-map,
lg-edge_wf,
int_seg_wf,
member-less_than,
is-dag_wf,
labeled-graph_wf
Latex:
\mforall{}[T,S:Type]. \mforall{}[f:T {}\mrightarrow{} S]. \mforall{}[g:LabeledGraph(T)]. is-dag(lg-map(f;g)) supposing is-dag(g)
Date html generated:
2015_07_23-AM-11_03_29
Last ObjectModification:
2015_01_28-PM-11_33_52
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