Nuprl Lemma : es-E-interface_functionality
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. E(X) ⊆r E(Y) supposing ∀e:E. ((↑e ∈b X) ⇒ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
es-E-interface: E(X),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
E(X) \msubseteq{}r E(Y) supposing \mforall{}e:E. ((\muparrow{}e \mmember{}\msubb{} X) {}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2016_05_16-PM-02_51_50
Last ObjectModification:
2015_12_29-AM-11_20_41
Theory : event-ordering
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