Nuprl Lemma : es-fix_property
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:E(X) ⟶ E(X).
((∀x:E(X). f x c≤ x) ⇒ (∀e:E(X). (((f f**(e)) = f**(e) ∈ E(X)) ∧ f**(e) is f*(e))))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-fix: f**(e),
es-causle: e c≤ e',
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
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],
es-fix: f**(e),
and: P ∧ Q,
cand: A c∧ B
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(X). (((f f**(e)) = f**(e)) \mwedge{} f**(e) is f*(e))))
Date html generated:
2016_05_16-PM-10_17_48
Last ObjectModification:
2015_12_29-AM-11_16_16
Theory : event-ordering
Home
Index