Nuprl Lemma : eclass1-classrel
∀[Info,B,C:Type]. ∀[f:Id ─→ B ─→ C]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ (f o X)(e);↓∃b:B. (b ∈ X(e) ∧ (v = (f loc(e) b) ∈ C)))
Proof
Definitions occuring in Statement :
eclass1: (f o X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
squash_wf,
exists_wf,
bag-member_wf,
es-loc_wf,
iff_weakening_uiff,
bag-map_wf,
bag-member-map,
uiff_wf,
classrel_wf,
eclass1_wf,
event-ordering+_subtype,
es-E_wf,
event-ordering+_wf,
eclass_wf,
Id_wf
\mforall{}[Info,B,C:Type]. \mforall{}[f:Id {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[X:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} (f o X)(e);\mdownarrow{}\mexists{}b:B. (b \mmember{} X(e) \mwedge{} (v = (f loc(e) b))))
Date html generated:
2015_07_17-PM-00_36_07
Last ObjectModification:
2015_01_27-PM-11_28_51
Home
Index