Nuprl Lemma : lg-add_wf
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[a,b:ℕlg-size(g)]. (lg-add(g;a;b) ∈ LabeledGraph(T))
Proof
Definitions occuring in Statement :
lg-add: lg-add(g;a;b),
lg-size: lg-size(g),
labeled-graph: LabeledGraph(T),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lg-add: lg-add(g;a;b),
labeled-graph: LabeledGraph(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
top: Top,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
nat: ℕ,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ,
spreadn: spread3,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
lg-size: lg-size(g),
le: A ≤ B,
less_than: a < b
Latex:
\mforall{}[T:Type]. \mforall{}[g:LabeledGraph(T)]. \mforall{}[a,b:\mBbbN{}lg-size(g)]. (lg-add(g;a;b) \mmember{} LabeledGraph(T))
Date html generated:
2016_05_17-AM-10_09_11
Last ObjectModification:
2016_01_18-AM-00_22_44
Theory : process-model
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