Nuprl Lemma : classrel-classfun-res-alt1
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[e:E]. ∀[v:T].
uiff(v ∈ X(e);if e ∈b X then v = X@e ∈ T else False fi ) 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,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False,
universe: Type,
equal: s = t ∈ T
Lemmas :
member-eclass_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
classrel-classfun-res,
classrel-implies-member,
equal_wf,
classfun-res_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[e:E]. \mforall{}[v:T].
uiff(v \mmember{} X(e);if e \mmember{}\msubb{} X then v = X@e else False fi ) supposing single-valued-classrel(es;X;T)
Date html generated:
2015_07_17-PM-00_21_55
Last ObjectModification:
2015_01_27-PM-11_40_42
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