Nuprl Lemma : es-closed-open-interval-decomp
∀[es:EO]. ∀[e1,e2:E]. [e1;e2) = [e1 / (e1, e2)] ∈ (E List) supposing (e1 <loc e2)
Proof
Definitions occuring in Statement :
es-closed-open-interval: [e;e'),
es-open-interval: (e, e'),
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
cons: [a / b],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-open-interval: (e, e'),
es-closed-open-interval: [e;e'),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
sq_type: SQType(T),
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s],
not: ¬A,
false: False,
uiff: uiff(P;Q),
bfalse: ff,
or: P ∨ Q,
cand: A c∧ B
Latex:
\mforall{}[es:EO]. \mforall{}[e1,e2:E]. [e1;e2) = [e1 / (e1, e2)] supposing (e1 <loc e2)
Date html generated:
2016_05_16-AM-09_37_15
Last ObjectModification:
2016_01_17-PM-01_27_47
Theory : new!event-ordering
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