Nuprl Lemma : es-E-interface_functionality-iff
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. uiff(E(X) ⊆r E(Y);{∀[e:E]. ↑e ∈b Y supposing ↑e ∈b X})
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,
uiff: uiff(P;Q),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
guard: {T},
universe: Type
Lemmas :
assert_witness,
in-eclass_wf,
assert_wf,
es-E_wf,
event-ordering+_subtype,
subtype_rel_wf,
subtype_rel_sets,
uall_wf,
isect_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
set_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
equal_wf
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
uiff(E(X) \msubseteq{}r E(Y);\{\mforall{}[e:E]. \muparrow{}e \mmember{}\msubb{} Y supposing \muparrow{}e \mmember{}\msubb{} X\})
Date html generated:
2015_07_17-PM-00_56_27
Last ObjectModification:
2015_01_27-PM-10_46_53
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