Nuprl Lemma : csm-path-eta
∀[pth,s:Top]. ((path-eta(pth))s ~ ((pth)p)s @ (q)s)
Proof
Definitions occuring in Statement :
path-eta: path-eta(pth),
cubicalpath-app: pth @ r,
cc-snd: q,
cc-fst: p,
csm-ap-term: (t)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
path-eta: path-eta(pth),
top: Top
Lemmas referenced :
csm-cubicalpath-app,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[pth,s:Top]. ((path-eta(pth))s \msim{} ((pth)p)s @ (q)s)
Date html generated:
2017_01_10-AM-08_54_53
Last ObjectModification:
2016_12_16-PM-04_28_34
Theory : cubical!type!theory
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