Nuprl Lemma : id-fiber-center_wf
∀[X:j⊢]. ∀[T:{X ⊢ _}]. (id-fiber-center(X;T) ∈ {X.T ⊢ _:Σ (T)p (Path_((T)p)p (q)p q)})
Proof
Definitions occuring in Statement :
id-fiber-center: id-fiber-center(X;T),
path-type: (Path_A a b),
cubical-sigma: Σ A B,
cc-snd: q,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
id-fiber-center: id-fiber-center(X;T),
subtype_rel: A ⊆r B,
squash: ↓T,
prop: ℙ,
all: ∀x:A. B[x],
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
cubical-type: {X ⊢ _},
cc-fst: p,
csm-ap-type: (AF)s,
csm-id: 1(X),
csm-ap: (s)x
Lemmas referenced :
cubical-pair_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
csm-ap-type_wf,
cc-fst_wf,
path-type_wf,
csm-ap-term_wf,
cc-snd_wf,
cubical-type_wf,
cubical_set_wf,
cubical-refl_wf,
cubical-term_wf,
squash_wf,
true_wf,
csm-id-adjoin_wf,
equal_wf,
istype-universe,
csm-path-type,
subtype_rel_self,
iff_weakening_equal,
csm_id_adjoin_fst_type_lemma,
csm_id_adjoin_fst_term_lemma,
csm-ap-id-term,
cc_snd_csm_id_adjoin_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
lambdaEquality_alt,
imageElimination,
universeEquality,
dependent_functionElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
Error :memTop,
setElimination,
rename,
hyp_replacement
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[T:\{X \mvdash{} \_\}]. (id-fiber-center(X;T) \mmember{} \{X.T \mvdash{} \_:\mSigma{} (T)p (Path\_((T)p)p (q)p q)\})
Date html generated:
2020_05_20-PM-03_30_36
Last ObjectModification:
2020_04_07-PM-05_47_43
Theory : cubical!type!theory
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