Nuprl Lemma : member-es-fix-prior-fixedpoints
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:E(X) ⟶ E(X). ((∀x:E(X). f x c≤ x) ⇒ (∀e:E(X). (f**(e) ∈ prior-f-fixedpoints(e))))
Proof
Definitions occuring in Statement :
es-prior-fixedpoints: prior-f-fixedpoints(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-fix: f**(e),
es-causle: e c≤ e',
l_member: (x ∈ l),
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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
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-prior-fixedpoints: prior-f-fixedpoints(e),
not: ¬A,
false: False,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
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**(e) \mmember{} prior-f-fixedpoints(e))))
Date html generated:
2016_05_17-AM-07_23_47
Last ObjectModification:
2015_12_28-PM-11_57_12
Theory : event-ordering
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