Nuprl Lemma : fun-connected-relation
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:E(X) ─→ E(X).
∀[R:E(X) ─→ E(X) ─→ ℙ]
(Trans(E(X);e',e.R[e';e])
⇒ Refl(E(X);e',e.R[e';e])
⇒ (∀x:E(X). R[f x;x])
⇒ (∀e',e:E(X). (e' is f*(e) ⇒ R[e';e])))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
trans: Trans(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
so_apply: x[s1;s2],
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-induction,
fun-connected_wf,
not_wf,
equal_wf,
all_wf,
refl_wf,
trans_wf,
es-E-interface_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
and_wf
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:E(X) {}\mrightarrow{} E(X).
\mforall{}[R:E(X) {}\mrightarrow{} E(X) {}\mrightarrow{} \mBbbP{}]
(Trans(E(X);e',e.R[e';e])
{}\mRightarrow{} Refl(E(X);e',e.R[e';e])
{}\mRightarrow{} (\mforall{}x:E(X). R[f x;x])
{}\mRightarrow{} (\mforall{}e',e:E(X). (e' is f*(e) {}\mRightarrow{} R[e';e])))
Date html generated:
2015_07_17-PM-01_01_30
Last ObjectModification:
2015_01_27-PM-10_42_08
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