Nuprl Lemma : classrel-classfun-res-alt2
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[e:E]. ∀[v:T].
uiff(v ∈ X(e);(↑e ∈b X) ∧ (v = X@e ∈ T)) supposing single-valued-classrel(es;X;T)
Proof
Definitions occuring in Statement :
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
member-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,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Lemmas :
assert_witness,
member-eclass_wf,
classrel_wf,
assert_wf,
classfun-res_wf,
classrel-implies-member,
classrel-classfun-res
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mmember{} X(e);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (v = X@e)) supposing single-valued-classrel(es;X;T)
Date html generated:
2015_07_17-PM-00_22_02
Last ObjectModification:
2015_01_27-PM-11_38_48
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