Nuprl Lemma : csm-ap-comp-type-sq2
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[s1,s2:Top]. (((A)s2)s1 ~ (A)s2 o s1)
Proof
Definitions occuring in Statement :
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
csm-comp: G o F,
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_set: CubicalSet,
csm-ap-type: (AF)s,
pscm-ap-type: (AF)s,
csm-ap: (s)x,
pscm-ap: (s)x,
csm-comp: G o F,
pscm-comp: G o F
Lemmas referenced :
pscm-ap-comp-type-sq2,
cube-cat_wf,
cubical-type-sq-presheaf-type
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule,
Error :memTop
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[s1,s2:Top]. (((A)s2)s1 \msim{} (A)s2 o s1)
Date html generated:
2020_05_20-PM-01_50_13
Last ObjectModification:
2020_04_03-PM-08_27_24
Theory : cubical!type!theory
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