Nuprl Lemma : DeMorgan-algebra-structure-subtype
DeMorganAlgebraStructure ⊆r BoundedLatticeStructure
Proof
Definitions occuring in Statement :
DeMorgan-algebra-structure: DeMorganAlgebraStructure,
bounded-lattice-structure: BoundedLatticeStructure,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
DeMorgan-algebra-structure: DeMorganAlgebraStructure,
bounded-lattice-structure: BoundedLatticeStructure,
record+: record+,
record-select: r.x,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uall: ∀[x:A]. B[x],
lattice-point: Point(l),
guard: {T}
Lemmas referenced :
subtype_rel_self,
lattice-point_wf,
bounded-lattice-structure-subtype,
DeMorgan-algebra-structure_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
dependentIntersectionElimination,
cut,
sqequalRule,
hypothesis,
applyEquality,
tokenEquality,
lemma_by_obid,
isectElimination,
thin,
functionEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
DeMorganAlgebraStructure \msubseteq{}r BoundedLatticeStructure
Date html generated:
2020_05_20-AM-08_55_08
Last ObjectModification:
2015_12_28-PM-01_56_11
Theory : lattices
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