Nuprl Lemma : fiber-subset
∀[X,T,A,f,a,phi:Top]. (X, phi ⊢ Fiber(f;a) ~ X ⊢ Fiber(f;a))
Proof
Definitions occuring in Statement :
cubical-fiber: Fiber(w;a),
context-subset: Gamma, phi,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
cubical-fiber: Fiber(w;a),
cubical-sigma: Σ A B,
member: t ∈ T,
top: Top
Lemmas referenced :
path-type-subset-adjoin,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache
Latex:
\mforall{}[X,T,A,f,a,phi:Top]. (X, phi \mvdash{} Fiber(f;a) \msim{} X \mvdash{} Fiber(f;a))
Date html generated:
2018_05_23-AM-09_40_42
Last ObjectModification:
2018_05_20-PM-06_40_59
Theory : cubical!type!theory
Home
Index