Nuprl Lemma : csm-ap-type-iota
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ((A)iota = A ∈ {X ⊢ _})
Proof
Definitions occuring in Statement :
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
subset-iota: iota,
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-type: {X ⊢ _},
subset-iota: iota,
csm-ap-type: (AF)s,
csm-ap: (s)x,
uimplies: b supposing a
Lemmas referenced :
cubical-type-equal,
I_cube_wf,
fset_wf,
nat_wf,
names-hom_wf,
cube-set-restriction_wf,
eta_conv,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
equalitySymmetry,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
productElimination,
sqequalRule,
dependent_pairEquality_alt,
lambdaEquality_alt,
applyEquality,
universeIsType,
hypothesis,
because_Cache,
inhabitedIsType,
functionIsType,
independent_isectElimination,
functionExtensionality_alt,
instantiate,
cumulativity,
universeEquality,
functionExtensionality
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. ((A)iota = A)
Date html generated:
2020_05_20-PM-01_49_56
Last ObjectModification:
2020_04_03-PM-08_27_30
Theory : cubical!type!theory
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