Nuprl Lemma : fl-all_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[phi:Point(face-lattice(T;eq))]. ∀[i:T]. ((∀i.phi) ∈ Point(face-lattice(T;eq)))
Proof
Definitions occuring in Statement :
fl-all: (∀i.phi),
face-lattice: face-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,
fl-all: (∀i.phi),
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
prop: ℙ,
and: P ∧ Q,
uimplies: b supposing a
Lemmas referenced :
deq_wf,
lattice-join_wf,
lattice-meet_wf,
equal_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
bounded-lattice-structure_wf,
subtype_rel_set,
face-lattice_wf,
lattice-point_wf,
fset_wf,
union-deq_wf,
deq-fset-member_wf,
bnot_wf,
band_wf,
fl-filter_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
unionEquality,
hypothesis,
inlEquality,
inrEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
applyEquality,
instantiate,
productEquality,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[phi:Point(face-lattice(T;eq))]. \mforall{}[i:T].
((\mforall{}i.phi) \mmember{} Point(face-lattice(T;eq)))
Date html generated:
2020_05_20-AM-08_52_51
Last ObjectModification:
2016_01_15-PM-05_40_14
Theory : lattices
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