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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