Nuprl Lemma : lconnects-transitive
∀p,q:IdLnk List. ∀i,j,k:Id. (∃r:IdLnk List. lconnects(r;i;k)) supposing (lconnects(q;j;k) and lconnects(p;i;j))
Proof
Definitions occuring in Statement :
lconnects: lconnects(p;i;j),
IdLnk: IdLnk,
Id: Id,
list: T List,
uimplies: b supposing a,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
lconnects: lconnects(p;i;j),
and: P ∧ Q,
lpath: lpath(p),
not: ¬A,
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,
subtract: n - m,
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
true: True,
ge: i ≥ j ,
le: A ≤ B,
cons: [a / b],
last: last(L),
select: L[n],
cand: A c∧ B,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
sq_type: SQType(T),
rev_implies: P ⇐ Q,
IdLnk: IdLnk,
Id: Id,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff
Latex:
\mforall{}p,q:IdLnk List. \mforall{}i,j,k:Id.
(\mexists{}r:IdLnk List. lconnects(r;i;k)) supposing (lconnects(q;j;k) and lconnects(p;i;j))
Date html generated:
2016_05_16-AM-10_58_32
Last ObjectModification:
2016_01_17-PM-03_53_20
Theory : event-ordering
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