Nuprl Lemma : cube_set_map_cumulativity
∀[G,H:j⊢]. (H j⟶ G ⊆r cube_set_map{j':l}(H; 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,
cubical_set: CubicalSet,
cube_set_map: A ⟶ B
Lemmas referenced :
psc_map_cumulativity,
cube-cat_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesis,
sqequalRule
Latex:
\mforall{}[G,H:j\mvdash{}]. (H j{}\mrightarrow{} G \msubseteq{}r cube\_set\_map\{j':l\}(H; G))
Date html generated:
2020_05_20-PM-01_40_49
Last ObjectModification:
2020_04_16-PM-05_34_32
Theory : cubical!type!theory
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