Nuprl Lemma : contractible-type-subset2
∀[X,A,B,C,phi:Top]. (X, phi.B.C ⊢ Contractible(A) ~ X.B.C ⊢ Contractible(A))
Proof
Definitions occuring in Statement :
contractible-type: Contractible(A),
context-subset: Gamma, phi,
cube-context-adjoin: X.A,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
contractible-type: Contractible(A),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
cubical-sigma-subset-adjoin2,
cubical-pi-subset-adjoin3,
path-type-subset-adjoin4,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache,
isect_memberFormation,
sqequalAxiom
Latex:
\mforall{}[X,A,B,C,phi:Top]. (X, phi.B.C \mvdash{} Contractible(A) \msim{} X.B.C \mvdash{} Contractible(A))
Date html generated:
2017_01_10-AM-08_55_52
Last ObjectModification:
2016_12_11-PM-02_12_31
Theory : cubical!type!theory
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