Nuprl Lemma : cal-point
∀[T,eq,P:Top].
(Point(constrained-antichain-lattice(T;eq;P)) ~ {ac:fset(fset(T))| (↑fset-antichain(eq;ac)) ∧ fset-all(ac;a.P a)} )
Proof
Definitions occuring in Statement :
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
lattice-point: Point(l),
fset-antichain: fset-antichain(eq;ac),
fset-all: fset-all(s;x.P[x]),
fset: fset(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lattice-point: Point(l),
record-select: r.x,
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),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
axiomSqEquality,
lemma_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[T,eq,P:Top].
(Point(constrained-antichain-lattice(T;eq;P)) \msim{} \{ac:fset(fset(T))|
(\muparrow{}fset-antichain(eq;ac)) \mwedge{} fset-all(ac;a.P a)\} )
Date html generated:
2020_05_20-AM-08_47_54
Last ObjectModification:
2016_01_15-PM-03_35_15
Theory : lattices
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