Nuprl Lemma : assert-lg-is-source
∀[T:Type]. ∀[g:LabeledGraph(T)]. ∀[i:ℕlg-size(g)].  uiff(↑lg-is-source(g;i);∀[j:ℕlg-size(g)]. (¬lg-edge(g;j;i)))
Proof
Definitions occuring in Statement : 
lg-is-source: lg-is-source(g;i)
, 
lg-edge: lg-edge(g;a;b)
, 
lg-size: lg-size(g)
, 
labeled-graph: LabeledGraph(T)
, 
int_seg: {i..j-}
, 
assert: ↑b
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
not: ¬A
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
lg-edge: lg-edge(g;a;b)
, 
lg-is-source: lg-is-source(g;i)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
int_seg: {i..j-}
, 
subtype_rel: A ⊆r B
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
ifthenelse: if b then t else f fi 
, 
not: ¬A
, 
false: False
, 
top: Top
, 
prop: ℙ
, 
rev_uimplies: rev_uimplies(P;Q)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
nat: ℕ
, 
lelt: i ≤ j < k
, 
less_than: a < b
, 
squash: ↓T
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
cons: [a / b]
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
Latex:
\mforall{}[T:Type].  \mforall{}[g:LabeledGraph(T)].  \mforall{}[i:\mBbbN{}lg-size(g)].
    uiff(\muparrow{}lg-is-source(g;i);\mforall{}[j:\mBbbN{}lg-size(g)].  (\mneg{}lg-edge(g;j;i)))
Date html generated:
2016_05_17-AM-10_10_46
Last ObjectModification:
2016_01_18-AM-00_22_14
Theory : process-model
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