Nuprl Lemma : classfun-res-eclass3
∀[Info,B,C:Type]. ∀[X:EClass(B ─→ C)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].
(eclass3(X;Y)@e = (X@e Y@e) ∈ C) supposing (X is functional at e and Y is functional at e)
Proof
Definitions occuring in Statement :
eclass3: eclass3(X;Y),
classfun-res: X@e,
es-functional-class-at: X is functional at e,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
sv-bag-only-combine,
bag-map_wf,
single-valued-classrel-implies-bag,
member-eclass-iff-size,
single-valued-bag-map,
bag-size-map,
equal_wf,
sv-bag-only_wf,
es-functional-class-at_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
sv-bag-only-map2,
iff_weakening_equal
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} C)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(eclass3(X;Y)@e = (X@e Y@e)) supposing (X is functional at e and Y is functional at e)
Date html generated:
2015_07_23-AM-11_29_19
Last ObjectModification:
2015_02_04-PM-04_44_40
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