Nuprl Lemma : es-fix-equal
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ⟶ E(X)].
∀[e:E(X)]. uiff(f**(e) = e ∈ E;(f e) = e ∈ E) supposing ∀x:E(X). f x c≤ x
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',
es-E: E,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
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,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
and: P ∧ Q,
uiff: uiff(P;Q),
guard: {T},
es-fix: f**(e),
fix: f**(x),
ycomb: Y,
not: ¬A,
false: False,
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
es-E: E,
label: ...$L... t,
bool: 𝔹,
unit: Unit,
it: ⋅,
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{}[e:E(X)]. uiff(f**(e) = e;(f e) = e) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2016_05_16-PM-10_18_01
Last ObjectModification:
2016_01_17-PM-07_27_17
Theory : event-ordering
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