Nuprl Lemma : fdl-hom-agrees
∀[X:Type]. ∀[L:BoundedDistributiveLattice]. ∀[f:X ⟶ Point(L)].
∀x:X. ((fdl-hom(L;f) free-dl-generator(x)) = (f x) ∈ Point(L))
Proof
Definitions occuring in Statement :
fdl-hom: fdl-hom(L;f),
free-dl-generator: free-dl-generator(x),
bdd-distributive-lattice: BoundedDistributiveLattice,
lattice-point: Point(l),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
free-dl-generator: free-dl-generator(x),
fdl-hom: fdl-hom(L;f),
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
uimplies: b supposing a,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
list_accum_cons_lemma,
list_accum_nil_lemma,
equal_wf,
squash_wf,
true_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,
lattice-meet_wf,
lattice-join_wf,
lattice-0_wf,
lattice-1-meet,
bdd-distributive-lattice-subtype-bdd-lattice,
iff_weakening_equal,
lattice-join-0,
bdd-distributive-lattice_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
applyEquality,
lambdaEquality,
imageElimination,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
instantiate,
productEquality,
independent_isectElimination,
setElimination,
rename,
functionExtensionality,
cumulativity,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
independent_functionElimination,
axiomEquality,
functionEquality
Latex:
\mforall{}[X:Type]. \mforall{}[L:BoundedDistributiveLattice]. \mforall{}[f:X {}\mrightarrow{} Point(L)].
\mforall{}x:X. ((fdl-hom(L;f) free-dl-generator(x)) = (f x))
Date html generated:
2020_05_20-AM-08_42_35
Last ObjectModification:
2017_07_28-AM-09_13_34
Theory : lattices
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