Nuprl Lemma : cubical-sigma-at
∀[X,A,B,I,a:Top]. (Σ A B(a) ~ u:A(a) × B((a;u)))
Proof
Definitions occuring in Statement :
cubical-sigma: Σ A B,
cc-adjoin-cube: (v;u),
cubical-type-at: A(a),
uall: ∀[x:A]. B[x],
top: Top,
product: x:A × B[x],
sqequal: s ~ t
Definitions unfolded in proof :
cubical-type-at: A(a),
presheaf-type-at: A(a),
cubical-sigma: Σ A B,
presheaf-sigma: Σ A B,
cc-adjoin-cube: (v;u),
psc-adjoin-set: (v;u),
cubical-type-ap-morph: (u a f),
presheaf-type-ap-morph: (u a f)
Lemmas referenced :
presheaf-sigma-at
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalRule,
sqequalReflexivity,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[X,A,B,I,a:Top]. (\mSigma{} A B(a) \msim{} u:A(a) \mtimes{} B((a;u)))
Date html generated:
2018_05_23-AM-08_58_39
Last ObjectModification:
2018_05_20-PM-06_07_03
Theory : cubical!type!theory
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