Nuprl Lemma : cube_set_map_cumulativity-i-j
∀[G,H:⊢]. (H ⟶ G ⊆r H ij⟶ G)
Proof
Definitions occuring in Statement :
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_self,
cube_set_map_wf,
cubical_set_cumulativity-i-j,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
hypothesisEquality,
applyEquality,
because_Cache,
axiomEquality,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[G,H:\mvdash{}]. (H {}\mrightarrow{} G \msubseteq{}r H ij{}\mrightarrow{} G)
Date html generated:
2020_05_20-PM-01_40_54
Last ObjectModification:
2020_04_16-PM-05_34_51
Theory : cubical!type!theory
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