Nuprl Lemma : free-dl-point
∀[T,eq:Top]. (Point(free-dist-lattice(T; eq)) ~ {ac:fset(fset(T))| ↑fset-antichain(eq;ac)} )
Proof
Definitions occuring in Statement :
free-dist-lattice: free-dist-lattice(T; eq),
lattice-point: Point(l),
fset-antichain: fset-antichain(eq;ac),
fset: fset(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-dist-lattice: free-dist-lattice(T; eq),
lattice-point: Point(l),
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,
axiomSqEquality,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[T,eq:Top]. (Point(free-dist-lattice(T; eq)) \msim{} \{ac:fset(fset(T))| \muparrow{}fset-antichain(eq;ac)\} )
Date html generated:
2020_05_20-AM-08_44_59
Last ObjectModification:
2015_12_28-PM-02_00_19
Theory : lattices
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