Nuprl Lemma : es-E-interface-conditional-subtype
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y,Z:EClass(Top)]. (E([X?Y]) ⊆ E(Z)) supposing ((E(Y) ⊆r E(Z)) and (E(X) ⊆r E(Z)))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
cond-class: [X?Y],
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
subtype: S ⊆ T,
universe: Type
Lemmas :
es-E-interface-conditional-subtype_rel,
es-E-interface_wf,
cond-class_wf,
top_wf,
subtype_rel_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y,Z:EClass(Top)].
(E([X?Y]) \msubseteq{} E(Z)) supposing ((E(Y) \msubseteq{}r E(Z)) and (E(X) \msubseteq{}r E(Z)))
Date html generated:
2015_07_17-PM-00_57_10
Last ObjectModification:
2015_01_27-PM-10_46_42
Home
Index