Nuprl Lemma : member-eclass-iff-size
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. (↑e ∈b X ⇐⇒ 0 < #(X es e))
Proof
Definitions occuring in Statement :
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
less_than: a < b,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
apply: f a,
natural_number: $n,
universe: Type,
bag-size: #(bs)
Definitions unfolded in proof :
member-eclass: e ∈b X,
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
nat: ℕ,
rev_implies: P ⇐ Q,
not: ¬A,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
ge: i ≥ j
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} 0 < \#(X es e))
Date html generated:
2016_05_16-PM-01_36_25
Last ObjectModification:
2016_01_17-PM-07_52_34
Theory : event-ordering
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