Nuprl Lemma : tagged-true-property
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T × 𝔹)]. ∀[e:E(Tagged_tt(X))]. ((↑e ∈b X) ∧ (↑(snd(X(e)))))
Proof
Definitions occuring in Statement :
es-tagged-true-class: Tagged_tt(X),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
assert: ↑b,
bool: 𝔹,
uall: ∀[x:A]. B[x],
pi2: snd(t),
and: P ∧ Q,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
es-E-interface: E(X),
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
Latex:
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T \mtimes{} \mBbbB{})]. \mforall{}[e:E(Tagged\_tt(X))].
((\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}(snd(X(e)))))
Date html generated:
2016_05_16-PM-10_32_19
Last ObjectModification:
2015_12_29-AM-11_01_17
Theory : event-ordering
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