Nuprl Lemma : context-1-subset
∀[Gamma:j⊢]. sub_cubical_set{j:l}(Gamma; Gamma, 1(𝔽))
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-1: 1(𝔽),
sub_cubical_set: Y ⊆ X,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sub_cubical_set: Y ⊆ X,
cubical_set: CubicalSet,
cube-cat: CubeCat,
ps_context: __⊢,
type-cat: TypeCat,
op-cat: op-cat(C),
cat-functor: Functor(C1;C2),
spreadn: spread4,
all: ∀x:A. B[x],
and: P ∧ Q,
cube_set_map: A ⟶ B,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
csm-id: 1(X),
face-1: 1(𝔽),
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
pi2: snd(t),
pi1: fst(t),
context-subset: Gamma, phi,
functor-ob: ob(F),
cubical-term-at: u(a),
compose: f o g,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
functor-arrow: arrow(F),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a
Lemmas referenced :
cubical_set_wf,
cat_ob_pair_lemma,
cat_arrow_triple_lemma,
cat_id_tuple_lemma,
cat_comp_tuple_lemma,
ob_pair_lemma,
I_cube_pair_redex_lemma,
lattice-1_wf,
face_lattice_wf,
fset_wf,
nat_wf,
arrow_pair_lemma,
cube_set_restriction_pair_lemma,
names-hom_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,
equal_wf,
lattice-meet_wf,
lattice-join_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
axiomEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeIsType,
instantiate,
extract_by_obid,
dependent_functionElimination,
thin,
Error :memTop,
setElimination,
rename,
productElimination,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
isectElimination,
hypothesisEquality,
applyEquality,
inhabitedIsType,
equalityIstype,
because_Cache,
lambdaFormation_alt,
functionIsType,
setIsType,
productEquality,
cumulativity,
isectEquality,
independent_isectElimination
Latex:
\mforall{}[Gamma:j\mvdash{}]. sub\_cubical\_set\{j:l\}(Gamma; Gamma, 1(\mBbbF{}))
Date html generated:
2020_05_20-PM-02_53_55
Last ObjectModification:
2020_04_04-PM-05_08_20
Theory : cubical!type!theory
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