Nuprl Lemma : fl_all-join
∀[I:fset(ℕ)]. ∀[i:ℕ]. ∀[a,b:Point(face_lattice(I+i))]. ((∀i.a ∨ b) = (∀i.a) ∨ (∀i.b) ∈ Point(face_lattice(I)))
Proof
Definitions occuring in Statement :
fl_all: (∀i.phi),
face_lattice: face_lattice(I),
add-name: I+i,
lattice-join: a ∨ b,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fl_all: (∀i.phi),
subtype_rel: A ⊆r B,
guard: {T},
bounded-lattice-hom: Hom(l1;l2),
and: P ∧ Q,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
names: names(I),
nat: ℕ,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_apply: x[s],
uimplies: b supposing a,
lattice-hom: Hom(l1;l2),
all: ∀x:A. B[x],
true: True,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
fl-all-hom_wf1,
bounded-lattice-hom_wf,
face_lattice_wf,
all_wf,
names_wf,
not_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,
fl0_wf,
names-subtype,
add-name_wf,
f-subset-add-name,
fl1_wf,
trivial-member-add-name1,
fset-member_wf,
nat_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
le_wf,
strong-subtype-self,
lattice-0_wf,
lattice-hom_wf,
fset_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
because_Cache,
sqequalRule,
productEquality,
functionEquality,
intEquality,
instantiate,
cumulativity,
universeEquality,
independent_isectElimination,
dependent_functionElimination,
dependent_set_memberEquality,
natural_numberEquality,
lambdaFormation,
independent_functionElimination,
isect_memberEquality,
axiomEquality,
functionExtensionality,
imageElimination,
productElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\mBbbN{}]. \mforall{}[a,b:Point(face\_lattice(I+i))]. ((\mforall{}i.a \mvee{} b) = (\mforall{}i.a) \mvee{} (\mforall{}i.b))
Date html generated:
2017_10_05-AM-01_16_21
Last ObjectModification:
2017_07_28-AM-09_32_36
Theory : cubical!type!theory
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