Nuprl Lemma : cubical-equiv-subset
∀[X,T,A,phi:Top]. (Equiv(T;A) ~ Equiv(T;A))
Proof
Definitions occuring in Statement :
cubical-equiv: Equiv(T;A),
context-subset: Gamma, phi,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
cubical-equiv: Equiv(T;A),
is-cubical-equiv: IsEquiv(T;A;w),
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
contractible-type-subset2,
top_wf,
cubical-sigma-subset,
cubical-fun-subset,
cubical-pi-subset,
cubical-fiber-subset-adjoin2
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberEquality,
voidElimination,
voidEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
isect_memberFormation,
sqequalAxiom
Latex:
\mforall{}[X,T,A,phi:Top]. (Equiv(T;A) \msim{} Equiv(T;A))
Date html generated:
2017_01_10-AM-08_57_23
Last ObjectModification:
2016_12_11-PM-02_18_07
Theory : cubical!type!theory
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