Nuprl Lemma : closed-cubical-universe_wf
cc𝕌 ∈ { * ⊢' _}
Proof
Definitions occuring in Statement :
closed-cubical-universe: cc𝕌,
closed-cubical-type: { * ⊢ _},
member: t ∈ T
Definitions unfolded in proof :
closed-cubical-universe: cc𝕌,
member: t ∈ T,
closed-cubical-type: { * ⊢ _},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
names-hom: I ⟶ J,
I_cube: A(I),
functor-ob: ob(F),
pi1: fst(t),
formal-cube: formal-cube(I),
fibrant-type: FibrantType(X),
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cube_set_map: A ⟶ B,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
cat-ob: cat-ob(C),
op-cat: op-cat(C),
spreadn: spread4,
cube-cat: CubeCat,
fset: fset(T),
quotient: x,y:A//B[x; y],
cat-arrow: cat-arrow(C),
pi2: snd(t),
type-cat: TypeCat,
cat-comp: cat-comp(C),
compose: f o g
Lemmas referenced :
fibrant-type_wf_formal-cube,
fset_wf,
nat_wf,
csm-fibrant-type_wf,
formal-cube_wf1,
context-map_wf,
subtype_rel_self,
I_cube_wf,
names-hom_wf,
equal_wf,
squash_wf,
true_wf,
istype-universe,
csm-fibrant-type-id,
nh-id_wf,
context-map-1,
iff_weakening_equal,
context-map-comp,
csm-fibrant-comp,
cube_set_map_wf,
nh-comp_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
lambdaEquality_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
universeIsType,
dependent_functionElimination,
applyEquality,
instantiate,
cumulativity,
universeEquality,
inhabitedIsType,
because_Cache,
functionIsType,
lambdaFormation_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
independent_pairFormation,
hyp_replacement,
applyLambdaEquality,
productIsType,
equalityIstype
Latex:
cc\mBbbU{} \mmember{} \{ * \mvdash{}' \_\}
Date html generated:
2020_05_20-PM-07_05_46
Last ObjectModification:
2020_04_25-PM-00_12_01
Theory : cubical!type!theory
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