Nuprl Lemma : cubical-sigma-subset-adjoin
∀[X,A,B,T,phi:Top]. (Σ A B ~ Σ A B)
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
cubical-sigma: Σ A B,
cube-context-adjoin: X.A,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
top: Top,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf,
cubical-sigma-normalize
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberEquality,
voidElimination,
voidEquality,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
extract_by_obid,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X,A,B,T,phi:Top]. (\mSigma{} A B \msim{} \mSigma{} A B)
Date html generated:
2018_05_23-AM-09_29_28
Last ObjectModification:
2018_05_20-PM-06_27_55
Theory : cubical!type!theory
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