Nuprl Lemma : path-eta-id-adjoin
∀[G,u,pth:Top]. ((path-eta(pth))[u] ~ pth @ u)
Proof
Definitions occuring in Statement :
path-eta: path-eta(pth),
cubicalpath-app: pth @ r,
csm-id-adjoin: [u],
csm-ap-term: (t)s,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
path-eta: path-eta(pth),
member: t ∈ T,
top: Top,
cubicalpath-app: pth @ r,
all: ∀x:A. B[x],
cubical-app: app(w; u),
csm-id: 1(X),
csm-ap-term: (t)s,
csm-ap: (s)x
Lemmas referenced :
csm-cubicalpath-app,
csm_id_adjoin_fst_term_lemma,
cc_snd_csm_id_adjoin_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
dependent_functionElimination,
because_Cache
Latex:
\mforall{}[G,u,pth:Top]. ((path-eta(pth))[u] \msim{} pth @ u)
Date html generated:
2017_01_10-AM-08_54_19
Last ObjectModification:
2017_01_02-AM-10_11_21
Theory : cubical!type!theory
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