Nuprl Lemma : free-dl-inc_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. (free-dl-inc(x) ∈ Point(free-dist-lattice(T; eq)))
Proof
Definitions occuring in Statement :
free-dl-inc: free-dl-inc(x),
free-dist-lattice: free-dist-lattice(T; eq),
lattice-point: Point(l),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-dl-inc: free-dl-inc(x),
top: Top,
prop: ℙ
Lemmas referenced :
free-dl-point,
fset-antichain-singleton,
fset-singleton_wf,
fset_wf,
assert_wf,
fset-antichain_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
dependent_set_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. (free-dl-inc(x) \mmember{} Point(free-dist-lattice(T; eq)))
Date html generated:
2016_05_18-AM-11_30_19
Last ObjectModification:
2015_12_28-PM-02_00_30
Theory : lattices
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