Nuprl Lemma : face-lattice1_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ((x=1) ∈ Point(face-lattice(T;eq)))
Proof
Definitions occuring in Statement :
face-lattice1: (x=1),
face-lattice: face-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,
so_lambda: λ2x.t[x],
so_apply: x[s],
face-lattice: face-lattice(T;eq),
all: ∀x:A. B[x]
Lemmas referenced :
free-dlwc-inc_wf,
union-deq_wf,
face-lattice-constraints_wf,
face-lattice1-is-inc,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
inrEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. ((x=1) \mmember{} Point(face-lattice(T;eq)))
Date html generated:
2020_05_20-AM-08_51_03
Last ObjectModification:
2015_12_28-PM-01_57_24
Theory : lattices
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