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
Lemmas :
es-fix-causle,
es-fix-equal-E-interface,
es-E-interface-property,
es-fix_wf2,
assert_wf,
in-eclass_wf,
not_wf,
equal_wf,
es-E_wf,
event-ordering+_subtype,
es-E-interface_wf,
all_wf,
es-causle_wf,
eclass_wf,
top_wf,
event-ordering+_wf
\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:
2015_07_17-PM-01_02_05
Last ObjectModification:
2015_01_27-PM-10_42_27
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