Nuprl Lemma : face-lattice-tube_wf
∀[I:fset(ℕ)]. ∀[phi:Point(face_lattice(I))]. ∀[j:ℕ]. (face-lattice-tube(I;phi;j) ∈ Point(face_lattice(I+j)))
Proof
Definitions occuring in Statement :
face-lattice-tube: face-lattice-tube(I;phi;j),
face_lattice: face_lattice(I),
add-name: I+i,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-lattice-tube: face-lattice-tube(I;phi;j),
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,
all: ∀x:A. B[x],
lattice-point: Point(l),
record-select: r.x,
face_lattice: face_lattice(I),
face-lattice: face-lattice(T;eq),
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
record-update: r[x := v],
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
bfalse: ff,
btrue: tt,
I_cube: A(I),
functor-ob: functor-ob(F),
pi1: fst(t),
face-presheaf: 𝔽,
names: names(I),
nat: ℕ
Lemmas referenced :
fl1_wf,
strong-subtype-self,
le_wf,
strong-subtype-set3,
strong-subtype-deq-subtype,
int-deq_wf,
nat_wf,
fset-member_wf,
trivial-member-add-name1,
fl0_wf,
face-lattice-constraints_wf,
fset-contains-none_wf,
fset-all_wf,
names-deq_wf,
union-deq_wf,
fset-antichain_wf,
assert_wf,
names_wf,
fset_wf,
subtype_rel_self,
f-subset-add-name,
nc-s_wf,
face-presheaf_wf,
cube-set-restriction_wf,
lattice-meet_wf,
equal_wf,
lattice-point_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
bounded-lattice-structure_wf,
subtype_rel_set,
add-name_wf,
face_lattice_wf,
lattice-join_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
applyEquality,
instantiate,
lambdaEquality,
productEquality,
cumulativity,
universeEquality,
independent_isectElimination,
dependent_functionElimination,
setEquality,
unionEquality,
dependent_set_memberEquality,
intEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[phi:Point(face\_lattice(I))]. \mforall{}[j:\mBbbN{}].
(face-lattice-tube(I;phi;j) \mmember{} Point(face\_lattice(I+j)))
Date html generated:
2016_05_18-PM-00_19_42
Last ObjectModification:
2016_02_18-PM-05_11_23
Theory : cubical!type!theory
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