Nuprl Lemma : es-fix-last-prior-fixedpoints
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ─→ E(X)].
∀[e:E(X)]. (last(prior-f-fixedpoints(e)) = f**(e) ∈ E(X)) 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',
last: last(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,
equal: s = t ∈ T
Lemmas :
es-prior-fixedpoints-fix,
es-E-interface_wf,
all_wf,
es-causle_wf,
event-ordering+_subtype,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
es-fix_wf2,
es-eq-E_wf,
assert_wf,
bnot_wf,
not_wf,
equal_wf,
assert_elim,
btrue_neq_bfalse,
es-fix_wf,
subtype_rel-equal,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-es-eq-E-2,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
subtype_top,
last_append,
es-prior-fixedpoints_wf,
eclass-val_wf2,
es-prior-interface_wf,
subtype_rel_list,
cons_wf,
nil_wf,
null_cons_lemma,
bfalse_wf,
null_wf3,
es-E-interface-property,
last_wf,
last_singleton,
iff_weakening_equal,
assert_functionality_wrt_uiff,
es-fix_property,
equal_functionality_wrt_subtype_rel2
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e:E(X)]. (last(prior-f-fixedpoints(e)) = f**(e)) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2015_07_21-PM-03_52_27
Last ObjectModification:
2015_02_04-PM-06_11_51
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