Nuprl Lemma : dM-hom-unique
∀[I:fset(ℕ)]. ∀[L:BoundedDistributiveLattice]. ∀[eqL:EqDecider(Point(L))]. ∀[g,h:Hom(dM(I);L)].
g = h ∈ Hom(dM(I);L) supposing ∀i:names(I). (((g <i>) = (h <i>) ∈ Point(L)) ∧ ((g <1-i>) = (h <1-i>) ∈ Point(L)))
Proof
Definitions occuring in Statement :
dM_opp: <1-x>,
dM_inc: <x>,
dM: dM(I),
names: names(I),
bdd-distributive-lattice: BoundedDistributiveLattice,
bounded-lattice-hom: Hom(l1;l2),
lattice-point: Point(l),
fset: fset(T),
deq: EqDecider(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_apply: x[s],
bounded-lattice-hom: Hom(l1;l2),
lattice-hom: Hom(l1;l2),
DeMorgan-algebra: DeMorganAlgebra,
guard: {T},
dM: dM(I),
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq),
all: ∀x:A. B[x],
dminc: <i>,
dM_inc: <x>,
dmopp: <1-i>,
dM_opp: <1-x>
Lemmas referenced :
all_wf,
names_wf,
equal_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,
dM_inc_wf,
dM_opp_wf,
bounded-lattice-hom_wf,
dM_wf,
DeMorgan-algebra-structure_wf,
DeMorgan-algebra-structure-subtype,
subtype_rel_transitivity,
DeMorgan-algebra-axioms_wf,
deq_wf,
bdd-distributive-lattice_wf,
fset_wf,
nat_wf,
free-dist-lattice-hom-unique2,
union-deq_wf,
names-deq_wf,
free-dma-hom-is-lattice-hom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
productEquality,
applyEquality,
instantiate,
cumulativity,
universeEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
hyp_replacement,
lambdaFormation,
unionElimination,
dependent_functionElimination,
productElimination
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[L:BoundedDistributiveLattice]. \mforall{}[eqL:EqDecider(Point(L))]. \mforall{}[g,h:Hom(dM(I);L)].
g = h supposing \mforall{}i:names(I). (((g <i>) = (h <i>)) \mwedge{} ((g ə-i>) = (h ə-i>)))
Date html generated:
2017_10_05-AM-00_59_29
Last ObjectModification:
2017_07_28-AM-09_25_20
Theory : cubical!type!theory
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