Nuprl Lemma : cc-adjoin-cube-restriction
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[J,K,g,v,u:Top]. (g((v;u)) ~ (g(v);(u v g)))
Proof
Definitions occuring in Statement :
cc-adjoin-cube: (v;u),
cube-context-adjoin: X.A,
cubical-type-ap-morph: (u a f),
cubical-type: {X ⊢ _},
cube-set-restriction: f(s),
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-type: {X ⊢ _},
cubical-type-ap-morph: (u a f),
cc-adjoin-cube: (v;u),
cube-context-adjoin: X.A,
pi2: snd(t),
cube-set-restriction: f(s),
pi1: fst(t)
Lemmas referenced :
top_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
hypothesis,
sqequalAxiom,
lemma_by_obid,
isect_memberEquality,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[J,K,g,v,u:Top]. (g((v;u)) \msim{} (g(v);(u v g)))
Date html generated:
2016_06_16-PM-05_40_56
Last ObjectModification:
2015_12_28-PM-04_35_06
Theory : cubical!sets
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