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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
trans: Trans(T;x,y.E[x; y]),
guard: {T},
refl: Refl(T;x,y.E[x; y]),
uimplies: b supposing a
Latex:
\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:
2016_05_16-PM-10_19_57
Last ObjectModification:
2015_12_29-AM-11_13_37
Theory : event-ordering
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