Nuprl Lemma : iseg-es-hist
∀[Info:Type]
∀es:EO+(Info). ∀e1,e2:E. ∀L:Info List.
(L ≤ es-hist(es;e1;e2) ⇒ ∃e∈[e1,e2].L = es-hist(es;e1;e) ∈ (Info List)) supposing
((¬(L = [] ∈ (Info List))) and
(loc(e1) = loc(e2) ∈ Id))
Proof
Definitions occuring in Statement :
es-hist: es-hist(es;e1;e2),
event-ordering+: EO+(Info),
existse-between2: ∃e∈[e1,e2].P[e],
es-loc: loc(e),
es-E: E,
Id: Id,
iseg: l1 ≤ l2,
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
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,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s],
not: ¬A,
false: False,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
es-hist: es-hist(es;e1;e2),
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
top: Top,
uiff: uiff(P;Q),
cand: A c∧ B,
es-E: E,
es-base-E: es-base-E(es),
existse-between2: ∃e∈[e1,e2].P[e],
exists: ∃x:A. B[x],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}e1,e2:E. \mforall{}L:Info List.
(L \mleq{} es-hist(es;e1;e2) {}\mRightarrow{} \mexists{}e\mmember{}[e1,e2].L = es-hist(es;e1;e)) supposing
((\mneg{}(L = [])) and
(loc(e1) = loc(e2)))
Date html generated:
2016_05_16-PM-01_21_11
Last ObjectModification:
2016_01_17-PM-07_54_06
Theory : event-ordering
Home
Index