Nuprl Lemma : fun-connected-causle
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:E(X) ─→ E(X). ((∀x:E(X). f x c≤ x) ⇒ (∀e,e':E(X). (e' is f*(e) ⇒ e' c≤ e)))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-causle: e c≤ e',
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
fun-connected: y is f*(x)
Lemmas :
fun-connected_wf,
es-E-interface_wf,
all_wf,
es-causle_wf,
event-ordering+_subtype,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
fun-connected-relation,
es-causle_transitivity,
es-causle_weakening_eq
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:E(X) {}\mrightarrow{} E(X).
((\mforall{}x:E(X). f x c\mleq{} x) {}\mRightarrow{} (\mforall{}e,e':E(X). (e' is f*(e) {}\mRightarrow{} e' c\mleq{} e)))
Date html generated:
2015_07_17-PM-01_01_39
Last ObjectModification:
2015_01_27-PM-10_42_58
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