Nuprl Lemma : interface-part-subtype
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[g:⋂es:EO+(Info). (E(X) ⟶ Id)]. ∀[i:Id]. ∀[es:EO+(Info)]. (E((X|g=i)) ⊆r E(X))
Proof
Definitions occuring in Statement :
es-interface-part: (X|g=i),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
prop: ℙ,
top: Top,
all: ∀x:A. B[x],
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
es-E-interface: E(X),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[g:\mcap{}es:EO+(Info). (E(X) {}\mrightarrow{} Id)]. \mforall{}[i:Id]. \mforall{}[es:EO+(Info)].
(E((X|g=i)) \msubseteq{}r E(X))
Date html generated:
2016_05_17-AM-08_09_50
Last ObjectModification:
2015_12_28-PM-11_13_35
Theory : event-ordering
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