Nuprl Lemma : bag-member-classfun-res
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[e:E].
(X@e ↓∈ X es e) supposing (single-valued-classrel(es;X;T) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
universe: Type,
bag-member: x ↓∈ bs
Definitions unfolded in proof :
single-valued-classrel: single-valued-classrel(es;X;T),
all: ∀x:A. B[x],
member: t ∈ T,
classrel: v ∈ X(e),
classfun-res: X@e,
classfun: X(e),
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
single-valued-bag: single-valued-bag(b;T),
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bag-member: x ↓∈ bs,
squash: ↓T
Latex:
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[e:E].
(X@e \mdownarrow{}\mmember{} X es e) supposing (single-valued-classrel(es;X;T) and (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_16-PM-01_44_42
Last ObjectModification:
2016_01_17-PM-07_49_30
Theory : event-ordering
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