Nuprl Lemma : fl-vertex_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[u:T + T]. (fl-vertex(u) ∈ Point(face-lattice(T;eq)))
Proof
Definitions occuring in Statement :
fl-vertex: fl-vertex(u),
face-lattice: face-lattice(T;eq),
lattice-point: Point(l),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fl-vertex: fl-vertex(u),
face-lattice0: (x=0),
face-lattice1: (x=1)
Lemmas referenced :
deq_wf,
face-lattice1_wf,
face-lattice0_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
unionElimination,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[u:T + T]. (fl-vertex(u) \mmember{} Point(face-lattice(T;eq)))
Date html generated:
2020_05_20-AM-08_51_27
Last ObjectModification:
2016_01_19-PM-05_18_44
Theory : lattices
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