Nuprl Lemma : univ-a_wf
∀[G:j⊢]. ∀[A,B:{G ⊢ _:c𝕌}]. (UA ∈ {G ⊢ _:(Equiv(decode(A);decode(B)) ⟶ (Path_c𝕌 A B))})
Proof
Definitions occuring in Statement :
univ-a: UA,
universe-decode: decode(t),
cubical-universe: c𝕌,
cubical-equiv: Equiv(T;A),
path-type: (Path_A a b),
cubical-fun: (A ⟶ B),
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,
subtype_rel: A ⊆r B,
guard: {T},
univ-a: UA,
all: ∀x:A. B[x],
uimplies: b supposing a
Lemmas referenced :
cubical-equiv_wf,
universe-decode_wf,
csm-ap-term-universe,
cubical_set_cumulativity-i-j,
cube-context-adjoin_wf,
cubical-type-cumulativity2,
cc-fst_wf,
cubical-lam_wf,
cubical-type-cumulativity,
path-type_wf,
cubical-universe_wf,
istype-cubical-universe-term,
cubical_set_wf,
csm-path-type,
cubical-term-eqcd,
csm-cubical-universe,
equiv-path_wf,
cc-snd_wf,
csm-cubical-equiv,
csm-universe-decode
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
instantiate,
applyEquality,
sqequalRule,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaEquality_alt,
hyp_replacement,
universeIsType,
dependent_functionElimination,
independent_isectElimination,
Error :memTop
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,B:\{G \mvdash{} \_:c\mBbbU{}\}]. (UA \mmember{} \{G \mvdash{} \_:(Equiv(decode(A);decode(B)) {}\mrightarrow{} (Path\_c\mBbbU{} A B))\})
Date html generated:
2020_05_20-PM-07_30_47
Last ObjectModification:
2020_04_28-PM-10_56_54
Theory : cubical!type!theory
Home
Index