Nuprl Lemma : csm-cubical-app
∀[w,u,s:Top]. ((app(w; u))s ~ app((w)s; (u)s))
Proof
Definitions occuring in Statement :
cubical-app: app(w; 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],
member: t ∈ T,
top: Top,
csm-ap-term: (t)s,
pscm-ap-term: (t)s,
cubical-app: app(w; u),
presheaf-app: app(w; u),
cube-cat: CubeCat,
all: ∀x:A. B[x],
csm-ap: (s)x,
pscm-ap: (s)x
Lemmas referenced :
pscm-presheaf-app,
cat_id_tuple_lemma
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
dependent_functionElimination,
hypothesis
Latex:
\mforall{}[w,u,s:Top]. ((app(w; u))s \msim{} app((w)s; (u)s))
Date html generated:
2018_05_23-AM-09_11_06
Last ObjectModification:
2018_05_20-PM-06_10_35
Theory : cubical!type!theory
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