Nuprl Lemma : lpath-members-connected
∀[p:IdLnk List]. ∀[i:ℕ||p||]. ∀[j:ℕi + 1]. lconnects(l_interval(p;j;i);source(p[j]);source(p[i])) supposing lpath(p)
Proof
Definitions occuring in Statement :
lconnects: lconnects(p;i;j),
lpath: lpath(p),
lsrc: source(l),
IdLnk: IdLnk,
l_interval: l_interval(l;j;i),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
lconnects: lconnects(p;i;j),
and: P ∧ Q,
lpath: lpath(p),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
cand: A c∧ B,
true: True,
subtract: n - m,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
sq_type: SQType(T)
Latex:
\mforall{}[p:IdLnk List]. \mforall{}[i:\mBbbN{}||p||]. \mforall{}[j:\mBbbN{}i + 1].
lconnects(l\_interval(p;j;i);source(p[j]);source(p[i])) supposing lpath(p)
Date html generated:
2016_05_16-AM-10_56_59
Last ObjectModification:
2016_01_17-PM-03_52_29
Theory : event-ordering
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