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;(f e) = e) supposing x:E(X). f x c
x
Proof not projected
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
Definitions :
so_lambda: 
x y.t[x; y],
so_lambda: x.t[x],
prop: 
,
member: t 
T,
es-E-interface: E(X),
true: True,
ifthenelse: if b then t else f fi ,
btrue: tt,
assert: 
b,
uimplies: b supposing a,
and: P 
Q,
uiff: uiff(P;Q),
guard: {T},
bfalse: ff,
implies: P 
Q,
all: x:A. B[x],
ycomb: Y,
fix: f**(x),
es-fix: f**(e),
eqof: eqof(d),
so_apply: x[s1;s2],
so_apply: x[s],
uall: [x:A]. B[x],
sq_type: SQType(T),
cand: A c B,
unit: Unit,
bool: 
,
false: False,
not: 
A,
subtype: S 
T,
it: 
Lemmas :
event-ordering+_wf,
top_wf,
eclass_wf,
es-causle_wf,
all_wf,
es-E-interface_wf,
equal_wf,
es-E-interface-subtype_rel,
es-fix_wf2,
event-ordering+_inc,
es-E_wf,
and_wf,
assert_wf,
in-eclass_wf,
assert_elim,
bool_subtype_base,
subtype_base_sq,
es-fix_property,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
assert-deq,
eqtt_to_assert,
uiff_transitivity,
not_wf,
bnot_wf,
bool_wf,
es-eq_wf,
eqof_wf,
es-eq_wf-interface
\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:
2012_01_23-PM-12_24_09
Last ObjectModification:
2011_12_13-PM-01_32_51
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