Nuprl Lemma : es-prior-fixedpoints-unequal
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ─→ E(X)].
∀[e,e':E(X)].
(¬(f**(e) ∈ prior-f-fixedpoints(e'))) supposing ((¬(e' = f**(e) ∈ E)) and (e' ∈ prior-f-fixedpoints(e)))
supposing ∀x:E(X). f x c≤ x
Proof
Definitions occuring in Statement :
es-prior-fixedpoints: prior-f-fixedpoints(e),
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,
l_member: (x ∈ l),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
not: ¬A,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
l_member_wf,
es-prior-fixedpoints_wf,
subtype_rel_list,
es-E_wf,
event-ordering+_subtype,
all_wf,
es-causle_wf,
es-E-interface_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
es-fix-last-prior-fixedpoints,
property-from-l_member,
equal_wf,
sq_stable__equal,
es-fix-sqequal,
es-fix-equal-E-interface,
and_wf,
in-eclass_wf,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_wf,
equal_functionality_wrt_subtype_rel2,
not_wf,
es-prior-fixedpoints-iseg,
es-prior-fixedpoints-non-null,
es-prior-fixedpoints-no_repeats,
list_wf,
last_wf,
iseg_wf,
null_wf3,
no_repeats_wf,
before_last,
iseg_is_sublist,
l_before_sublist,
last-not-before,
es-fix_wf2
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e,e':E(X)].
(\mneg{}(f**(e) \mmember{} prior-f-fixedpoints(e'))) supposing
((\mneg{}(e' = f**(e))) and
(e' \mmember{} prior-f-fixedpoints(e)))
supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2015_07_21-PM-03_54_06
Last ObjectModification:
2015_01_27-PM-06_04_01
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