Nuprl Lemma : is-pair-prior
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. ∀[e:E]. uiff(↑e ∈b X;Y;(↑e ∈b (X)') ∧ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
es-interface-pair-prior: X;Y,
es-prior-val: (X)',
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
es-interface-pair-prior: X;Y,
in-eclass: e ∈b X,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
assert: ↑b,
top: Top,
eq_int: (i =z j),
true: True,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)]. \mforall{}[e:E]. uiff(\muparrow{}e \mmember{}\msubb{} X;Y;(\muparrow{}e \mmember{}\msubb{} (X)') \mwedge{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2016_05_17-AM-07_16_56
Last ObjectModification:
2015_12_29-AM-00_02_12
Theory : event-ordering
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