Nuprl Lemma : dma-neg_wf
∀[dma:DeMorganAlgebraStructure]. ∀[x:Point(dma)]. (¬(x) ∈ Point(dma))
Proof
Definitions occuring in Statement :
dma-neg: ¬(x),
DeMorgan-algebra-structure: DeMorganAlgebraStructure,
lattice-point: Point(l),
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dma-neg: ¬(x),
DeMorgan-algebra-structure: DeMorganAlgebraStructure,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
lattice-point: Point(l),
guard: {T},
uimplies: b supposing a
Lemmas referenced :
subtype_rel_self,
lattice-point_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
DeMorgan-algebra-structure_wf,
bounded-lattice-structure_wf,
lattice-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
instantiate,
lemma_by_obid,
isectElimination,
universeEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
lambdaEquality,
axiomEquality,
independent_isectElimination,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[dma:DeMorganAlgebraStructure]. \mforall{}[x:Point(dma)]. (\mneg{}(x) \mmember{} Point(dma))
Date html generated:
2016_05_18-AM-11_46_52
Last ObjectModification:
2015_12_28-PM-01_56_07
Theory : lattices
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