Nuprl Lemma : contractible-type-at
∀[X,A,I,rho:Top]. (Contractible(A)(rho) ~ u:A(rho) × cubical-pi-family(X.A;(A)p;(Path_((A)p)p (q)p q);I;(rho;u)))
Proof
Definitions occuring in Statement :
contractible-type: Contractible(A),
path-type: (Path_A a b),
cubical-pi-family: cubical-pi-family(X;A;B;I;a),
cc-snd: q,
cc-fst: p,
cc-adjoin-cube: (v;u),
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
csm-ap-type: (AF)s,
cubical-type-at: A(a),
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
contractible-type: Contractible(A),
cubical-pi: ΠA B,
cubical-sigma: Σ A B,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
cubical_type_at_pair_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,A,I,rho:Top].
(Contractible(A)(rho) \msim{} u:A(rho) \mtimes{} cubical-pi-family(X.A;(A)p;(Path\_((A)p)p (q)p q);I;(rho;u)))
Date html generated:
2018_05_23-AM-09_39_12
Last ObjectModification:
2018_05_20-PM-06_39_41
Theory : cubical!type!theory
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