Nuprl Lemma : fin-powerset-lattice_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. (fin-powerset-lattice(T;eq) ∈ DistributiveLattice)
Proof
Definitions occuring in Statement :
fin-powerset-lattice: fin-powerset-lattice(T;eq),
distributive-lattice: DistributiveLattice,
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,
fin-powerset-lattice: fin-powerset-lattice(T;eq),
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
so_apply: x[s1;s2],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
mk-distributive-lattice_wf,
fset_wf,
fset-intersection_wf,
fset-union_wf,
equal_wf,
squash_wf,
true_wf,
fset-intersection-commutes,
iff_weakening_equal,
fset-union-commutes,
fset-intersection-associative,
fset-union-associative,
fset-absorption1,
fset-absorption2,
fset-distributive,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
independent_isectElimination,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
independent_functionElimination,
isect_memberEquality,
axiomEquality,
independent_pairFormation
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. (fin-powerset-lattice(T;eq) \mmember{} DistributiveLattice)
Date html generated:
2020_05_20-AM-08_47_25
Last ObjectModification:
2017_07_28-AM-09_15_02
Theory : lattices
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