Nuprl Lemma : es-prior-fixedpoints-unequal
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ⟶ E(X)].
∀[e,e':E(X)].
(¬(f**(e) ∈ prior-f-fixedpoints(e'))) supposing ((¬(e' = f**(e) ∈ E)) and (e' ∈ prior-f-fixedpoints(e)))
supposing ∀x:E(X). f x c≤ x
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',
es-E: E,
l_member: (x ∈ l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
subtype_rel: A ⊆r B,
es-E-interface: E(X),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
rev_implies: P ⇐ Q,
not: ¬A,
false: False,
top: Top,
iff: P ⇐⇒ Q
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e,e':E(X)].
(\mneg{}(f**(e) \mmember{} prior-f-fixedpoints(e'))) supposing
((\mneg{}(e' = f**(e))) and
(e' \mmember{} prior-f-fixedpoints(e)))
supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2016_05_17-AM-07_26_16
Last ObjectModification:
2015_12_28-PM-11_54_41
Theory : event-ordering
Home
Index