Nuprl Lemma : free-dist-lattice-hom-unique2
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:BoundedDistributiveLattice]. ∀[eqL:EqDecider(Point(L))].
∀[g,h:Hom(free-dist-lattice(T; eq);L)].
g = h ∈ Hom(free-dist-lattice(T; eq);L) supposing ∀x:T. ((g free-dl-inc(x)) = (h free-dl-inc(x)) ∈ Point(L))
Proof
Definitions occuring in Statement :
free-dl-inc: free-dl-inc(x),
free-dist-lattice: free-dist-lattice(T; eq),
bdd-distributive-lattice: BoundedDistributiveLattice,
bounded-lattice-hom: Hom(l1;l2),
lattice-point: Point(l),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bounded-lattice-hom: Hom(l1;l2),
and: P ∧ Q,
lattice-hom: Hom(l1;l2),
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
top: Top,
guard: {T},
bdd-lattice: BoundedLattice,
cand: A c∧ B,
implies: P ⇒ Q,
all: ∀x:A. B[x],
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
compose: f o g
Lemmas referenced :
uall_wf,
lattice-point_wf,
free-dist-lattice_wf,
subtype_rel_set,
bounded-lattice-structure_wf,
lattice-structure_wf,
lattice-axioms_wf,
bounded-lattice-structure-subtype,
bounded-lattice-axioms_wf,
equal_wf,
lattice-meet_wf,
lattice-join_wf,
lattice-0_wf,
lattice-1_wf,
all_wf,
free-dl-inc_wf,
bounded-lattice-hom_wf,
bdd-distributive-lattice_wf,
deq_wf,
free-dl-point,
free-dl-basis,
bdd-distributive-lattice-subtype-bdd-lattice,
deq-fset_wf,
fset_wf,
strong-subtype-deq-subtype,
assert_wf,
fset-antichain_wf,
strong-subtype-set2,
lattice-hom-fset-join,
subtype_rel_transitivity,
bdd-lattice_wf,
fset-image_wf,
lattice-fset-meet_wf,
decidable__equal_free-dl,
lattice-fset-join_wf,
squash_wf,
decidable_wf,
decidable-equal-deq,
true_wf,
iff_weakening_equal,
fset-image-compose,
lattice-hom-fset-meet
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
productElimination,
hypothesis,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
applyEquality,
sqequalRule,
instantiate,
lambdaEquality,
productEquality,
universeEquality,
because_Cache,
independent_isectElimination,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
axiomEquality,
voidElimination,
voidEquality,
hyp_replacement,
applyLambdaEquality,
setEquality,
independent_pairFormation,
independent_functionElimination,
lambdaFormation,
dependent_functionElimination,
natural_numberEquality,
imageElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L:BoundedDistributiveLattice]. \mforall{}[eqL:EqDecider(Point(L))].
\mforall{}[g,h:Hom(free-dist-lattice(T; eq);L)].
g = h supposing \mforall{}x:T. ((g free-dl-inc(x)) = (h free-dl-inc(x)))
Date html generated:
2020_05_20-AM-08_46_52
Last ObjectModification:
2017_07_28-AM-09_14_56
Theory : lattices
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