Nuprl Lemma : cube-context-adjoin-I_cube
∀[Gamma,A,I:Top]. (Gamma.A(I) ~ alpha:Gamma(I) × A(alpha))
Proof
Definitions occuring in Statement :
cube-context-adjoin: X.A,
cubical-type-at: A(a),
I_cube: A(I),
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
I_cube: A(I),
I_set: A(I),
cube-context-adjoin: X.A,
psc-adjoin: X.A,
cubical-type-at: A(a),
presheaf-type-at: A(a),
cube-set-restriction: f(s),
psc-restriction: f(s),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f)
Lemmas referenced :
psc-adjoin-I_set
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalRule,
sqequalReflexivity,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[Gamma,A,I:Top]. (Gamma.A(I) \msim{} alpha:Gamma(I) \mtimes{} A(alpha))
Date html generated:
2018_05_23-AM-08_47_36
Last ObjectModification:
2018_05_20-PM-05_57_23
Theory : cubical!type!theory
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