Nuprl Lemma : es-fix-causl
∀[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) < e) supposing ¬((f e) = e ∈ 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',
es-causl: (e < e'),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
es-causle: e c≤ e',
or: P ∨ Q,
not: ¬A,
uiff: uiff(P;Q),
and: P ∧ Q,
es-E-interface: E(X),
prop: ℙ,
false: False,
es-causl: (e < e'),
squash: ↓T,
subtype_rel: A ⊆r B,
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{} (\mforall{}e:E(X). (f**(e) < e) supposing \mneg{}((f e) = e)))
Date html generated:
2016_05_16-PM-10_20_41
Last ObjectModification:
2016_01_17-PM-07_26_05
Theory : event-ordering
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