Nuprl Lemma : single-eclass-val
∀[T:Type]. ∀[A:es:EO+(T) ─→ E ─→ Type]. ∀[X:EClass(A[es;e])]. ∀[eo:EO+(T)]. ∀[e:E].
(X eo e) = {X(e)} ∈ bag(A[eo;e]) supposing ↑e ∈b X
Proof
Definitions occuring in Statement :
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
single-bag: {x},
bag: bag(T)
Lemmas :
assert_wf,
in-eclass_wf,
dep-eclass_subtype_rel,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
eclass_wf,
bag_wf,
bag-size-one,
assert_of_eq_int,
eq_int_wf,
bag-size_wf,
nat_wf
\mforall{}[T:Type]. \mforall{}[A:es:EO+(T) {}\mrightarrow{} E {}\mrightarrow{} Type]. \mforall{}[X:EClass(A[es;e])]. \mforall{}[eo:EO+(T)]. \mforall{}[e:E].
(X eo e) = \{X(e)\} supposing \muparrow{}e \mmember{}\msubb{} X
Date html generated:
2015_07_17-PM-00_40_36
Last ObjectModification:
2015_01_27-PM-11_10_26
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