Nuprl Lemma : es-prior-fixedpoints-non-null
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:E(X) ─→ E(X)].
∀[e:E(X)]. (¬↑null(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',
null: null(as),
assert: ↑b,
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
Lemmas :
member-es-fix-prior-fixedpoints,
assert_wf,
null_wf3,
es-prior-fixedpoints_wf,
subtype_rel_list,
es-E-interface_wf,
es-E_wf,
event-ordering+_subtype,
top_wf,
all_wf,
es-causle_wf,
eclass_wf,
assert_elim,
member-implies-null-eq-bfalse,
es-fix_wf2,
btrue_neq_bfalse
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:E(X) {}\mrightarrow{} E(X)].
\mforall{}[e:E(X)]. (\mneg{}\muparrow{}null(prior-f-fixedpoints(e))) supposing \mforall{}x:E(X). f x c\mleq{} x
Date html generated:
2015_07_21-PM-03_52_38
Last ObjectModification:
2015_01_27-PM-05_58_28
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