Nuprl Lemma : context-subset_wf
∀[Gamma:j⊢]. ∀[phi:{Gamma ⊢ _:𝔽}]. Gamma, phi j⊢
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical_set: CubicalSet,
ps_context: __⊢,
cat-functor: Functor(C1;C2),
context-subset: Gamma, phi,
type-cat: TypeCat,
cat-arrow: cat-arrow(C),
op-cat: op-cat(C),
cat-ob: cat-ob(C),
cube-cat: CubeCat,
spreadn: spread4,
pi1: fst(t),
pi2: snd(t),
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,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cubical-type-at: A(a),
face-type: 𝔽,
constant-cubical-type: (X),
I_cube: A(I),
functor-ob: ob(F),
face-presheaf: 𝔽,
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,
cat-comp: cat-comp(C),
cat-id: cat-id(C),
all: ∀x:A. B[x],
compose: f o g
Lemmas referenced :
I_cube_wf,
fset_wf,
nat_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
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,
lattice-meet_wf,
lattice-join_wf,
face-term-at-restriction-eq-1,
lattice-1_wf,
subtype_rel_self,
iff_weakening_equal,
cube-set-restriction_wf,
cubical-term-at_wf,
face-type_wf,
names-hom_wf,
nh-id_wf,
cube-set-restriction-id,
nh-comp_wf,
cube-set-restriction-comp,
cat-ob_wf,
op-cat_wf,
cube-cat_wf,
cat-arrow_wf,
type-cat_wf,
cat-id_wf,
cat-comp_wf,
cubical-term_wf,
cubical_set_wf,
face_lattice-point_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
sqequalRule,
dependent_pairEquality_alt,
lambdaEquality_alt,
setEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
productEquality,
cumulativity,
isectEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
inhabitedIsType,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
equalityIstype,
setIsType,
functionIsType,
independent_pairFormation,
lambdaFormation_alt,
functionExtensionality,
dependent_functionElimination,
productIsType,
axiomEquality,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. Gamma, phi j\mvdash{}
Date html generated:
2020_05_20-PM-02_44_56
Last ObjectModification:
2020_04_05-PM-01_42_57
Theory : cubical!type!theory
Home
Index