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
Lemmas :
is-interface-part,
assert_wf,
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
es-E-interface_wf,
es-interface-part_wf,
event-ordering+_wf,
Id_wf,
eclass_wf
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:
2015_07_21-PM-04_20_48
Last ObjectModification:
2015_01_27-PM-05_17_31
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