Nuprl Lemma : csm-ap-type-subset-iota
∀[X:j⊢]. ∀[A:{X ⊢ _}]. ∀[s:Top]. (((A)s)iota ~ (A)s)
Proof
Definitions occuring in Statement :
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
subset-iota: iota,
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 ⊢ _},
csm-ap-type: (AF)s,
subset-iota: iota,
csm-ap: (s)x
Lemmas referenced :
istype-top,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
hypothesis,
axiomSqEquality,
extract_by_obid,
isect_memberEquality_alt,
isectElimination,
hypothesisEquality,
isectIsTypeImplies,
inhabitedIsType,
universeIsType,
instantiate
Latex:
\mforall{}[X:j\mvdash{}]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[s:Top]. (((A)s)iota \msim{} (A)s)
Date html generated:
2020_05_20-PM-01_49_15
Last ObjectModification:
2020_04_03-PM-08_26_48
Theory : cubical!type!theory
Home
Index