Nuprl Lemma : cubical-fiber-at
∀[X,T,A,w,a,I,rho:Top]. (Fiber(w;a)(rho) ~ u:T(rho) × (Path_(A)p (a)p app((w)p; q))((rho;u)))
Proof
Definitions occuring in Statement :
cubical-fiber: Fiber(w;a),
path-type: (Path_A a b),
cubical-app: app(w; u),
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,
cubical-type-at: A(a),
cubical-fiber: Fiber(w;a),
cubical-sigma: Σ A B,
pi1: fst(t)
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
extract_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,T,A,w,a,I,rho:Top]. (Fiber(w;a)(rho) \msim{} u:T(rho) \mtimes{} (Path\_(A)p (a)p app((w)p; q))((rho;u)))
Date html generated:
2018_05_23-AM-09_40_21
Last ObjectModification:
2018_05_20-PM-06_40_39
Theory : cubical!type!theory
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