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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