Nuprl Lemma : bind-class-rel-weak
∀[Info,T,S:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[Y:T ─→ EClass(S)]. ∀[e:E]. ∀[v:S].
(v ∈ X >u> Y[u](e) ⇐⇒ ↓∃e':{e':E| e' ≤loc e } . ∃u:T. (u ∈ X(e') ∧ v ∈ Y[u](e)))
Proof
Definitions occuring in Statement :
bind-class: X >x> Y[x],
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
uall: ∀[x:A]. B[x],
so_apply: x[s],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
squash: ↓T,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
universe: Type
Lemmas :
bind-class-rel,
classrel_wf,
bind-class_wf,
squash_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
es-le_wf,
eo-forward_wf,
member-eo-forward-E,
equal_wf,
Id_wf,
es-loc_wf,
eclass_wf,
event-ordering+_wf
\mforall{}[Info,T,S:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[Y:T {}\mrightarrow{} EClass(S)]. \mforall{}[e:E]. \mforall{}[v:S].
(v \mmember{} X >u> Y[u](e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}e':\{e':E| e' \mleq{}loc e \} . \mexists{}u:T. (u \mmember{} X(e') \mwedge{} v \mmember{} Y[u](e)))
Date html generated:
2015_07_17-PM-00_46_10
Last ObjectModification:
2015_01_27-PM-11_05_37
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