Nuprl Lemma : member-eclass-eclass3
∀[Info,B,C:Type]. ∀[X:EClass(B ─→ C)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(↑e ∈b eclass3(X;Y);(↑e ∈b X) ∧ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
eclass3: eclass3(X;Y),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert-member-eclass,
eclass3-classrel,
classrel_wf,
assert_witness,
member-eclass_wf,
assert_wf,
eclass3_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} C)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} eclass3(X;Y);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2015_07_23-AM-11_28_22
Last ObjectModification:
2015_01_28-PM-11_13_06
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