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),
cubical-sigma: Σ A B,
pi1: fst(t),
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,A,B,I,a:Top]. (\mSigma{} A B(a) \msim{} u:A(a) \mtimes{} B((a;u)))
Date html generated:
2016_06_16-PM-05_44_55
Last ObjectModification:
2015_12_28-PM-04_33_00
Theory : cubical!sets
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