Nuprl Lemma : transEquiv_wf
∀[G:j⊢]. ∀[A,B:{G ⊢ _:c𝕌}]. ∀[p:{G ⊢ _:(Path_c𝕌 A B)}]. (transEquiv{i:l}(G;A;p) ∈ {G ⊢ _:Equiv(decode(A);decode(B))})
Proof
Definitions occuring in Statement :
transEquiv: transEquiv{i:l}(G;A;p),
universe-decode: decode(t),
cubical-universe: c𝕌,
cubical-equiv: Equiv(T;A),
path-type: (Path_A 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,
all: ∀x:A. B[x],
cubical-lam: cubical-lam(X;b),
csm-id: 1(X),
csm-ap-term: (t)s,
cc-snd: q,
csm-id-adjoin: [u],
csm-ap: (s)x,
csm-adjoin: (s;u),
pi2: snd(t),
cc-fst: p,
pi1: fst(t),
guard: {T},
uimplies: b supposing a,
transEquiv: transEquiv{i:l}(G;A;p)
Lemmas referenced :
cc-snd_wf,
cubical-universe_wf,
csm-cubical-universe,
csm-ap-term-universe,
cubical_set_cumulativity-i-j,
cube-context-adjoin_wf,
cubical-type-cumulativity2,
cc-fst_wf,
equivTerm_wf,
cubical-lam_wf,
cubical-subst_wf,
istype-cubical-term,
path-type_wf,
istype-cubical-universe-term,
cubical_set_wf,
decode-equivTerm,
cubical-beta,
csm-equivTerm,
csm-id-adjoin-wf,
csm-ap-id-term,
csm-id_wf,
universe-decode_wf,
cubical-term-eqcd,
cubical-id-equiv_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
hypothesisEquality,
hypothesis,
sqequalRule,
Error :memTop,
applyEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
universeIsType,
rename,
lambdaFormation_alt,
inhabitedIsType,
applyLambdaEquality,
independent_isectElimination,
lambdaEquality_alt,
hyp_replacement
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[A,B:\{G \mvdash{} \_:c\mBbbU{}\}]. \mforall{}[p:\{G \mvdash{} \_:(Path\_c\mBbbU{} A B)\}].
(transEquiv\{i:l\}(G;A;p) \mmember{} \{G \mvdash{} \_:Equiv(decode(A);decode(B))\})
Date html generated:
2020_05_20-PM-07_34_26
Last ObjectModification:
2020_04_30-PM-00_08_18
Theory : cubical!type!theory
Home
Index