Nuprl Lemma : fdl-hom_wf1
∀[X:Type]. ∀[L:BoundedDistributiveLattice]. ∀[f:X ⟶ Point(L)]. (fdl-hom(L;f) ∈ (X List List) ⟶ Point(L))
Proof
Definitions occuring in Statement :
fdl-hom: fdl-hom(L;f),
bdd-distributive-lattice: BoundedDistributiveLattice,
lattice-point: Point(l),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fdl-hom: fdl-hom(L;f),
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_wf,
list_wf,
lattice-point_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
uall_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
lattice-0_wf,
lattice-1_wf,
bdd-distributive-lattice_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
instantiate,
productEquality,
because_Cache,
inhabitedIsType,
universeIsType,
independent_isectElimination,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
cumulativity,
isect_memberEquality_alt,
isectIsTypeImplies,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[L:BoundedDistributiveLattice]. \mforall{}[f:X {}\mrightarrow{} Point(L)].
(fdl-hom(L;f) \mmember{} (X List List) {}\mrightarrow{} Point(L))
Date html generated:
2020_05_20-AM-08_27_44
Last ObjectModification:
2018_11_13-AM-10_13_59
Theory : lattices
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