Nuprl Lemma : classfun-res-eclass1
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[f:Id ─→ B ─→ C]. ∀[es:EO+(Info)]. ∀[e:E].
((f o X)@e = (f loc(e) X@e) ∈ C) supposing (single-valued-classrel(es;X;B) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
eclass1: (f o X),
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
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-map2,
es-loc_wf,
single-valued-classrel-implies-bag,
member-eclass-iff-size,
single-valued-classrel_wf,
assert_wf,
member-eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Id_wf,
eclass_wf
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[f:Id {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
((f o X)@e = (f loc(e) X@e)) supposing (single-valued-classrel(es;X;B) and (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2015_07_23-AM-11_29_15
Last ObjectModification:
2015_01_28-PM-11_13_00
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