Nuprl Lemma : cc-snd-csm-adjoin
∀[Gamma,Delta:CubicalSet]. ∀[A:{Gamma ⊢ _}]. ∀[sigma:Delta ⟶ Gamma]. ∀[u:{Delta ⊢ _:(A)sigma}].
((q)(sigma;u) = u ∈ {Delta ⊢ _:(A)sigma})
Proof
Definitions occuring in Statement :
csm-adjoin: (s;u),
cc-snd: q,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:AF},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube-set-map: A ⟶ B,
cubical-set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-term: {X ⊢ _:AF},
csm-adjoin: (s;u),
csm-ap: (s)x,
pi2: snd(t),
cc-snd: q,
csm-ap-term: (t)s,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cubical-type: {X ⊢ _},
pi1: fst(t)
Lemmas referenced :
cubical-term_wf,
csm-ap-type_wf,
cube-set-map_wf,
cubical-type_wf,
cubical-set_wf,
I-cube_wf,
coordinate_name_wf,
list_wf,
name-morph_wf,
cube-set-restriction_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
equalitySymmetry,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality_alt,
hypothesis,
universeIsType,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
applyEquality,
functionExtensionality,
lambdaFormation_alt,
equalityIsType1,
equalityTransitivity,
dependent_functionElimination,
independent_functionElimination,
functionIsType,
because_Cache,
productElimination
Latex:
\mforall{}[Gamma,Delta:CubicalSet]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[sigma:Delta {}\mrightarrow{} Gamma]. \mforall{}[u:\{Delta \mvdash{} \_:(A)sigma\}].
((q)(sigma;u) = u)
Date html generated:
2019_11_05-PM-00_26_18
Last ObjectModification:
2018_11_08-PM-00_51_44
Theory : cubical!sets
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