Nuprl Lemma : csm-glue-comp
∀[G:j⊢]. ∀[K:Top]. ∀[A:{G ⊢ _}]. ∀[psi:{G ⊢ _:𝔽}]. ∀[T:{G, psi ⊢ _}]. ∀[cA,cT,f,tau:Top].
((comp(Glue [psi ⊢→ (T, f)] A) )tau ~ comp(Glue [(psi)tau ⊢→ ((T)tau, (f)tau)] (A)tau) )
Proof
Definitions occuring in Statement :
glue-comp: comp(Glue [phi ⊢→ (T, f)] A) ,
csm-comp-structure: (cA)tau,
context-subset: Gamma, phi,
face-type: 𝔽,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
csm-comp-structure: (cA)tau,
glue-comp: comp(Glue [phi ⊢→ (T, f)] A) ,
member: t ∈ T,
csm-ap-term: (t)s,
interval-type: 𝕀,
csm-comp: G o F,
csm-ap: (s)x,
compose: f o g,
cubical-type: {X ⊢ _},
csm-ap-type: (AF)s,
interval-1: 1(𝕀),
csm-id-adjoin: [u],
partial-term-1: u[1],
cc-fst: p,
cc-snd: q,
interval-0: 0(𝕀),
csm-id: 1(X),
csm-adjoin: (s;u)
Lemmas referenced :
csm-equiv-fun,
cubical-type_wf,
context-subset_wf,
istype-cubical-term,
face-type_wf,
istype-top,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :memTop,
hypothesisEquality,
hypothesis,
because_Cache,
setElimination,
rename,
productElimination,
universeIsType,
instantiate
Latex:
\mforall{}[G:j\mvdash{}]. \mforall{}[K:Top]. \mforall{}[A:\{G \mvdash{} \_\}]. \mforall{}[psi:\{G \mvdash{} \_:\mBbbF{}\}]. \mforall{}[T:\{G, psi \mvdash{} \_\}]. \mforall{}[cA,cT,f,tau:Top].
((comp(Glue [psi \mvdash{}\mrightarrow{} (T, f)] A) )tau \msim{} comp(Glue [(psi)tau \mvdash{}\mrightarrow{} ((T)tau, (f)tau)] (A)tau) )
Date html generated:
2020_05_20-PM-07_04_15
Last ObjectModification:
2020_04_21-PM-07_53_16
Theory : cubical!type!theory
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