Nuprl Lemma : assert-member-eclass
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. (↑e ∈b X ⇐⇒ ↓∃v:T. v ∈ X(e))
Proof
Definitions occuring in Statement :
classrel: v ∈ X(e),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
squash: ↓T,
universe: Type
Definitions unfolded in proof :
classrel: v ∈ X(e),
member-eclass: e ∈b X,
member: t ∈ T,
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
not: ¬A,
uiff: uiff(P;Q),
uimplies: b supposing a,
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}v:T. v \mmember{} X(e))
Date html generated:
2016_05_16-PM-01_36_16
Last ObjectModification:
2016_01_17-PM-07_51_55
Theory : event-ordering
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