Nuprl Lemma : es-prior-fixedpoints-iseg
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀f:E(X) ⟶ E(X).
((∀x:E(X). f x c≤ x)
⇒ (∀e,e':E(X). ((e' ∈ prior-f-fixedpoints(e)) ⇒ prior-f-fixedpoints(e') ≤ prior-f-fixedpoints(e))))
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',
iseg: l1 ≤ l2,
l_member: (x ∈ l),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
es-E-interface: E(X),
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
es-prior-fixedpoints: prior-f-fixedpoints(e),
uiff: uiff(P;Q),
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
label: ...$L... t,
es-causle: e c≤ e'
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}f:E(X) {}\mrightarrow{} E(X).
((\mforall{}x:E(X). f x c\mleq{} x)
{}\mRightarrow{} (\mforall{}e,e':E(X).
((e' \mmember{} prior-f-fixedpoints(e)) {}\mRightarrow{} prior-f-fixedpoints(e') \mleq{} prior-f-fixedpoints(e))))
Date html generated:
2016_05_17-AM-07_25_09
Last ObjectModification:
2016_01_17-PM-03_03_30
Theory : event-ordering
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