Nuprl Lemma : free-dlwc-point
∀[T,eq,Cs:Top].
(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x])) ~ {ac:fset(fset(T))|
(↑fset-antichain(eq;ac))
∧ fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))} )
Proof
Definitions occuring in Statement :
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
lattice-point: Point(l),
fset-antichain: fset-antichain(eq;ac),
fset-contains-none: fset-contains-none(eq;s;x.Cs[x]),
fset-all: fset-all(s;x.P[x]),
fset: fset(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
and: P ∧ Q,
set: {x:A| B[x]} ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
lattice-point: Point(l),
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
all: ∀x:A. B[x],
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
rec_select_update_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[T,eq,Cs:Top].
(Point(free-dist-lattice-with-constraints(T;eq;x.Cs[x]))
\msim{} \{ac:fset(fset(T))| (\muparrow{}fset-antichain(eq;ac)) \mwedge{} fset-all(ac;a.fset-contains-none(eq;a;x.Cs[x]))\} )
Date html generated:
2016_05_18-AM-11_32_55
Last ObjectModification:
2015_12_28-PM-01_59_03
Theory : lattices
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