Nuprl Lemma : univ-a_wf2
∀[G:j⊢]. (UA ∈ {G.c𝕌.c𝕌 ⊢ _:(Equiv(decode(q);decode((q)p)) ⟶ (Path_c𝕌 q (q)p))})
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),
cc-snd: q,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
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
Lemmas referenced :
cc-snd_wf,
cube-context-adjoin_wf,
cubical_set_cumulativity-i-j,
cubical-universe_wf,
cubical-type-cumulativity2,
csm-cubical-universe,
csm-ap-term_wf,
cc-fst_wf,
univ-a_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
universeIsType
Latex:
\mforall{}[G:j\mvdash{}]. (UA \mmember{} \{G.c\mBbbU{}.c\mBbbU{} \mvdash{} \_:(Equiv(decode(q);decode((q)p)) {}\mrightarrow{} (Path\_c\mBbbU{} q (q)p))\})
Date html generated:
2020_05_20-PM-07_31_02
Last ObjectModification:
2020_04_28-PM-11_17_32
Theory : cubical!type!theory
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