Nuprl Lemma : lpath_cons
∀[l:IdLnk]. ∀[p:IdLnk List].
uiff(lpath([l / p]);lpath(p)
∧ (destination(l) = source(hd(p)) ∈ Id) ∧ (¬(hd(p) = lnk-inv(l) ∈ IdLnk)) supposing ¬(||p|| = 0 ∈ ℤ))
Proof
Definitions occuring in Statement :
lpath: lpath(p),
ldst: destination(l),
lsrc: source(l),
lnk-inv: lnk-inv(l),
IdLnk: IdLnk,
Id: Id,
hd: hd(l),
length: ||as||,
cons: [a / b],
list: T List,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
all: ∀x:A. B[x],
or: P ∨ Q,
cons: [a / b],
top: Top,
guard: {T},
nat: ℕ,
le: A ≤ B,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
true: True,
listp: A List+,
lpath: lpath(p),
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
select: L[n],
cand: A c∧ B,
sq_type: SQType(T)
Latex:
\mforall{}[l:IdLnk]. \mforall{}[p:IdLnk List].
uiff(lpath([l / p]);lpath(p)
\mwedge{} (destination(l) = source(hd(p))) \mwedge{} (\mneg{}(hd(p) = lnk-inv(l))) supposing \mneg{}(||p|| = 0))
Date html generated:
2016_05_16-AM-10_56_49
Last ObjectModification:
2016_01_17-PM-03_51_10
Theory : event-ordering
Home
Index