Nuprl Lemma : es-prior-fixedpoints-no_repeats
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ─→ E(X)].
∀[e:E(X)]. no_repeats(E(X);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-causle: e c≤ e',
no_repeats: no_repeats(T;l),
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
Lemmas :
es-eq-E_wf,
event-ordering+_subtype,
bool_wf,
equal-wf-T-base,
assert_wf,
equal_wf,
es-E_wf,
bnot_wf,
not_wf,
no_repeats_singleton,
uiff_transitivity,
eqtt_to_assert,
assert-es-eq-E-2,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
no_repeats-append,
es-E-interface_wf,
es-prior-fixedpoints_wf,
eclass-val_wf2,
es-prior-interface_wf,
subtype_rel_list,
cons_wf,
nil_wf,
es-prior-interface-causl,
l_disjoint_singleton,
l_member_wf,
es-prior-fixedpoints-causle,
Id_wf,
es-loc-prior-interface,
es-loc_wf,
iff_weakening_equal,
es-causle-le,
eclass-val_wf,
es-locl_transitivity2,
es-locl_irreflexivity,
event-ordering+_wf,
es-prior-interface_wf0,
no_repeats_wf,
es-prior-fixedpoints-fix,
es-fix_wf2,
es-fix-causle,
es-fix-equal-E-interface,
es-E-interface-property,
in-eclass_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e:E(X)]. no\_repeats(E(X);prior-f-fixedpoints(e)) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2015_07_21-PM-03_53_32
Last ObjectModification:
2015_02_04-PM-06_12_10
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