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
Definitions unfolded in proof :
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
so_apply: x[s],
so_lambda: λ2x.t[x],
top: Top,
es-E-interface: E(X),
subtype_rel: A ⊆r B,
prop: ℙ,
false: False,
implies: P ⇒ Q,
not: ¬A,
uimplies: b supposing a,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
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:
2016_05_17-AM-07_24_25
Last ObjectModification:
2015_12_28-PM-11_52_31
Theory : event-ordering
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