Nuprl Lemma : lg-edge-add
∀[T:Type]
∀g:LabeledGraph(T). ∀i,j,a,b:ℕlg-size(g).
(lg-edge(lg-add(g;i;j);a;b) ⇐⇒ lg-edge(g;a;b) ∨ ((a = i ∈ ℤ) ∧ (b = j ∈ ℤ)))
Proof
Definitions occuring in Statement :
lg-edge: lg-edge(g;a;b),
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],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
lg-edge: lg-edge(g;a;b),
lg-add: lg-add(g;a;b),
lg-in-edges: lg-in-edges(g;x),
lg-size: lg-size(g),
top: Top,
labeled-graph: LabeledGraph(T),
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
int_seg: {i..j-},
uimplies: b supposing a,
prop: ℙ,
ge: i ≥ j ,
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,
implies: P ⇒ Q,
not: ¬A,
spreadn: spread3,
pi2: snd(t),
pi1: fst(t),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
iff: P ⇐⇒ Q,
cand: A c∧ B,
rev_implies: P ⇐ Q,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T
Latex:
\mforall{}[T:Type]
\mforall{}g:LabeledGraph(T). \mforall{}i,j,a,b:\mBbbN{}lg-size(g).
(lg-edge(lg-add(g;i;j);a;b) \mLeftarrow{}{}\mRightarrow{} lg-edge(g;a;b) \mvee{} ((a = i) \mwedge{} (b = j)))
Date html generated:
2016_05_17-AM-10_09_44
Last ObjectModification:
2016_01_18-AM-00_22_53
Theory : process-model
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