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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
not: ¬A,
false: False,
prop: ℙ,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
refl: Refl(T;x,y.E[x; y]),
and: P ∧ Q,
trans: Trans(T;x,y.E[x; y])
Latex:
\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:
2016_05_16-PM-10_19_44
Last ObjectModification:
2015_12_29-AM-11_14_12
Theory : event-ordering
Home
Index