Nuprl Lemma : member-eclass-iff-non-empty
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E]. (↑e ∈b X ⇐⇒ ¬((X es e) = {} ∈ bag(T)))
Proof
Definitions occuring in Statement :
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
apply: f a,
universe: Type,
equal: s = t ∈ T,
empty-bag: {},
bag: bag(T)
Definitions unfolded in proof :
member: t ∈ T,
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
not: ¬A,
false: False,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
bag-size: #(bs),
length: ||as||,
list_ind: list_ind,
empty-bag: {},
nil: [],
it: ⋅,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
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{} \mneg{}((X es e) = \{\}))
Date html generated:
2016_05_16-PM-01_36_37
Last ObjectModification:
2016_01_17-PM-07_51_43
Theory : event-ordering
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