Nuprl Lemma : csm+-ap-term-wf
∀[H,K:j⊢]. ∀[phi:{H ⊢ _:𝔽}]. ∀[A:{H, phi.𝕀 ⊢ _}]. ∀[tau:K j⟶ H]. ∀[t:{H, phi.𝕀 ⊢ _:A}].
((t)tau+ ∈ {K, (phi)tau.𝕀 ⊢ _:(A)tau+})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
interval-type: 𝕀,
csm+: tau+,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
csm-ap-type: (AF)s,
cubical-type: {X ⊢ _},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
cube_set_map: A ⟶ B,
psc_map: A ⟶ B,
nat-trans: nat-trans(C;D;F;G),
cat-ob: cat-ob(C),
pi1: fst(t),
op-cat: op-cat(C),
spreadn: spread4,
cube-cat: CubeCat,
fset: fset(T),
quotient: x,y:A//B[x; y],
cat-arrow: cat-arrow(C),
pi2: snd(t),
type-cat: TypeCat,
all: ∀x:A. B[x],
names-hom: I ⟶ J,
cat-comp: cat-comp(C),
compose: f o g
Lemmas referenced :
csm-ap-term_wf,
cube-context-adjoin_wf,
context-subset_wf,
cubical_set_cumulativity-i-j,
face-type_wf,
csm-face-type,
interval-type_wf,
csm+_wf_interval,
context-subset-map,
subtype_rel_self,
cube_set_map_wf,
cubical-term_wf,
cubical-type-cumulativity2,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
because_Cache,
axiomEquality,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[H,K:j\mvdash{}]. \mforall{}[phi:\{H \mvdash{} \_:\mBbbF{}\}]. \mforall{}[A:\{H, phi.\mBbbI{} \mvdash{} \_\}]. \mforall{}[tau:K j{}\mrightarrow{} H]. \mforall{}[t:\{H, phi.\mBbbI{} \mvdash{} \_:A\}].
((t)tau+ \mmember{} \{K, (phi)tau.\mBbbI{} \mvdash{} \_:(A)tau+\})
Date html generated:
2020_05_20-PM-03_06_38
Last ObjectModification:
2020_04_06-PM-00_03_29
Theory : cubical!type!theory
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