Nuprl Lemma : es-fix-order-preserving
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:E(X) ⟶ E(X).
((∀x:E(X). f x c≤ x) ⇒ global-order-preserving(es;X;f) ⇒ interface-order-preserving(es;X;λe.f**(e)))
Proof
Definitions occuring in Statement :
global-order-preserving: global-order-preserving(es;X;f),
interface-order-preserving: interface-order-preserving(es;X;f),
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,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
global-order-preserving: global-order-preserving(es;X;f),
interface-order-preserving: interface-order-preserving(es;X;f),
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
iff: P ⇐⇒ Q,
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
es-E-interface: E(X),
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
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{} global-order-preserving(es;X;f)
{}\mRightarrow{} interface-order-preserving(es;X;\mlambda{}e.f**(e)))
Date html generated:
2016_05_16-PM-10_20_54
Last ObjectModification:
2016_01_17-PM-07_29_27
Theory : event-ordering
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