Nuprl Lemma : csm-cubical-type-ap-morph
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[I,J,f,a,u,s:Top]. ((u a f) ~ (u (s)a f))
Proof
Definitions occuring in Statement :
csm-ap-type: (AF)s,
cubical-type-ap-morph: (u a f),
cubical-type: {X ⊢ _},
csm-ap: (s)x,
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
cubical-type: {X ⊢ _},
csm-ap: (s)x,
cubical-type-ap-morph: (u a f),
csm-ap-type: (AF)s,
pi2: snd(t),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
top_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
setElimination,
thin,
rename,
cut,
productElimination,
sqequalRule,
hypothesis,
lemma_by_obid,
because_Cache,
isectElimination,
hypothesisEquality,
isect_memberFormation,
introduction,
sqequalAxiom,
isect_memberEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[I,J,f,a,u,s:Top]. ((u a f) \msim{} (u (s)a f))
Date html generated:
2016_06_16-PM-05_39_51
Last ObjectModification:
2015_12_28-PM-04_35_48
Theory : cubical!sets
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