Nuprl Lemma : face-lattice_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. (face-lattice(T;eq) ∈ BoundedDistributiveLattice)
Proof
Definitions occuring in Statement :
face-lattice: face-lattice(T;eq),
bdd-distributive-lattice: BoundedDistributiveLattice,
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,
face-lattice: face-lattice(T;eq),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
free-dist-lattice-with-constraints_wf,
union-deq_wf,
face-lattice-constraints_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. (face-lattice(T;eq) \mmember{} BoundedDistributiveLattice)
Date html generated:
2016_05_18-AM-11_38_40
Last ObjectModification:
2015_12_28-PM-01_57_39
Theory : lattices
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