Nuprl Lemma : empty-cubical-subset-I_cube
∀[I,J:fset(ℕ)]. (¬I,0(J))
Proof
Definitions occuring in Statement :
cubical-subset: I,psi
,
face_lattice: face_lattice(I)
,
I_cube: A(I)
,
lattice-0: 0
,
fset: fset(T)
,
nat: ℕ
,
uall: ∀[x:A]. B[x]
,
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
not: ¬A
,
implies: P
⇒ Q
,
false: False
,
cubical-subset: I,psi
,
I_cube: A(I)
,
cube-cat: CubeCat
,
rep-sub-sheaf: rep-sub-sheaf(C;X;P)
,
functor-ob: ob(F)
,
pi1: fst(t)
,
all: ∀x:A. B[x]
,
top: Top
,
name-morph-satisfies: (psi f) = 1
,
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
,
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
,
face-presheaf: 𝔽
Lemmas referenced :
cat_arrow_triple_lemma,
equal_wf,
squash_wf,
true_wf,
lattice-point_wf,
face_lattice_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,
fl-morph-0,
subtype_rel_self,
iff_weakening_equal,
I_cube_wf,
cubical-subset_wf,
lattice-0_wf,
bdd-distributive-lattice_wf,
face-presheaf_wf,
small_cubical_set_subtype,
fset_wf,
nat_wf,
face-lattice-0-not-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
sqequalHypSubstitution,
sqequalRule,
extract_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
setElimination,
rename,
applyEquality,
lambdaEquality,
imageElimination,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
instantiate,
productEquality,
cumulativity,
because_Cache,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}[I,J:fset(\mBbbN{})]. (\mneg{}I,0(J))
Date html generated:
2018_05_23-AM-09_15_48
Last ObjectModification:
2018_05_20-PM-06_14_51
Theory : cubical!type!theory
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