{ [T:Type]. [g:LabeledGraph(T)]. [x:].
    lg-remove(g;x) ~ g supposing lg-size(g)  x }

{ Proof }



Definitions occuring in Statement :  lg-remove: lg-remove(g;n) lg-size: lg-size(g) labeled-graph: LabeledGraph(T) nat: uimplies: b supposing a uall: [x:A]. B[x] le: A  B universe: Type sqequal: s ~ t
Definitions :  member: t  T all: x:A. B[x] implies: P  Q lg-remove: lg-remove(g;n) nat: le: A  B top: Top not: A false: False subtype: S  T map: map(f;as) spreadn: spread3 ifthenelse: if b then t else f fi  filter: filter(P;l) bnot: b ycomb: Y reduce: reduce(f;k;as) btrue: tt prop: bfalse: ff labeled-graph: LabeledGraph(T) uall: [x:A]. B[x] uimplies: b supposing a int_seg: {i..j} bool: lelt: i  j < k unit: Unit iff: P  Q and: P  Q lg-size: lg-size(g) it:
Lemmas :  le_wf lg-size_wf nat_wf labeled-graph_wf int_seg_wf length_wf1 nth_tl_is_nil top_wf append-nil firstn_wf firstn_all eq_int_wf bool_wf iff_weakening_uiff uiff_transitivity assert_wf eqtt_to_assert assert_of_eq_int not_wf bnot_wf eqff_to_assert assert_of_bnot not_functionality_wrt_uiff le_int_wf assert_of_le_int lt_int_wf assert_functionality_wrt_uiff bnot_of_le_int assert_of_lt_int

\mforall{}[T:Type].  \mforall{}[g:LabeledGraph(T)].  \mforall{}[x:\mBbbN{}].    lg-remove(g;x)  \msim{}  g  supposing  lg-size(g)  \mleq{}  x


Date html generated: 2011_08_16-PM-06_37_17
Last ObjectModification: 2011_06_20-AM-01_56_53

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