Nuprl Lemma : is-tagged-true
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X:EClass(T × 𝔹)]. ∀[e:E].
uiff(↑e ∈b Tagged_tt(X);(↑e ∈b X) ∧ (↑(snd(X(e)))))
Proof
Definitions occuring in Statement :
es-tagged-true-class: Tagged_tt(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
pi2: snd(t),
and: P ∧ Q,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
es-tagged-true-class: Tagged_tt(X),
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,
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
uiff: uiff(P;Q),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
assert: ↑b,
ifthenelse: if b then t else f fi ,
true: True,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
pi2: snd(t),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bag-size: #(bs),
length: ||as||,
list_ind: list_ind,
empty-bag: {},
nil: []
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T \mtimes{} \mBbbB{})]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} Tagged\_tt(X);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}(snd(X(e)))))
Date html generated:
2016_05_16-PM-10_31_56
Last ObjectModification:
2016_01_17-PM-07_24_03
Theory : event-ordering
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