Nuprl Lemma : fl-point-sq
∀[T,eq:Top].
(Point(face-lattice(T;eq)) ~ {ac:fset(fset(T + T))|
(↑fset-antichain(union-deq(T;T;eq;eq);ac))
∧ fset-all(ac;a.fset-contains-none(union-deq(T;T;eq;
eq);a;x.face-lattice-constraints(x)))} )
Proof
Definitions occuring in Statement :
face-lattice: face-lattice(T;eq),
face-lattice-constraints: face-lattice-constraints(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),
union-deq: union-deq(A;B;a;b),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
set: {x:A| B[x]} ,
union: left + right,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-lattice: face-lattice(T;eq),
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
top_wf,
free-dlwc-point
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
axiomSqEquality,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[T,eq:Top].
(Point(face-lattice(T;eq))
\msim{} \{ac:fset(fset(T + T))|
(\muparrow{}fset-antichain(union-deq(T;T;eq;eq);ac))
\mwedge{} fset-all(ac;a.fset-contains-none(union-deq(T;T;eq;eq);a;x.face-lattice-constraints(x)))\} )
Date html generated:
2020_05_20-AM-08_51_11
Last ObjectModification:
2016_01_18-PM-11_31_19
Theory : lattices
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