Nuprl Lemma : dminc_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[i:T]. (<i> ∈ Point(free-DeMorgan-lattice(T;eq)))
Proof
Definitions occuring in Statement :
dminc: <i>,
free-DeMorgan-lattice: free-DeMorgan-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-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
dminc: <i>
Lemmas referenced :
free-dl-inc_wf,
union-deq_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,
inlEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[i:T]. (<i> \mmember{} Point(free-DeMorgan-lattice(T;eq)))
Date html generated:
2020_05_20-AM-08_54_10
Last ObjectModification:
2015_12_28-PM-01_56_28
Theory : lattices
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