Nuprl Lemma : es-closed-interval-vals-decomp
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A)]. ∀[e1,e2:E].
X[e1;e2]
= (if e1 <loc e2 ∧b e1 ∈b X then [X(e1)] else [] fi @ X(e1, e2) @ if e2 ∈b X then [X(e2)] else [] fi )
∈ (A List)
supposing e1 ≤loc e2
Proof
Definitions occuring in Statement :
es-closed-interval-vals: X[e1;e2],
es-prior-interval-vals: X(e1, e2),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-bless: e <loc e',
es-le: e ≤loc e' ,
es-E: E,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
es-closed-interval-vals: X[e1;e2],
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
ifthenelse: if b then t else f fi ,
band: p ∧b q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
bfalse: ff,
not: ¬A,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
guard: {T},
squash: ↓T,
true: True,
uiff: uiff(P;Q),
in-eclass: e ∈b X,
eq_int: (i =z j),
bag-size: #(bs),
length: ||as||,
list_ind: list_ind,
es-E-interface: E(X),
mapfilter: mapfilter(f;P;L),
es-prior-interval-vals: X(e1, e2),
false: False,
map: map(f;as),
filter: filter(P;l),
reduce: reduce(f;k;as),
es-open-interval: (e, e'),
es-before: before(e),
es-first: first(e),
bor: p ∨bq,
es-eq-E: e = e',
es-eq: es-eq(es),
eq_id: a = b,
id-deq: IdDeq,
atom2-deq: Atom2Deq,
eq_atom: eq_atom$n(x;y),
es-loc: loc(e),
record-select: r.x,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[e1,e2:E].
X[e1;e2]
= (if e1 <loc e2 \mwedge{}\msubb{} e1 \mmember{}\msubb{} X then [X(e1)] else [] fi
@ X(e1, e2)
@ if e2 \mmember{}\msubb{} X then [X(e2)] else [] fi )
supposing e1 \mleq{}loc e2
Date html generated:
2016_05_16-PM-10_26_19
Last ObjectModification:
2016_01_17-PM-07_33_11
Theory : event-ordering
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