Nuprl Lemma : csm-fibrant-type_wf
∀[G,H:j⊢]. ∀[s:H j⟶ G]. ∀[FT:FibrantType(G)]. (csm-fibrant-type(G;H;s;FT) ∈ FibrantType(H))
Proof
Definitions occuring in Statement :
csm-fibrant-type: csm-fibrant-type(G;H;s;FT),
fibrant-type: FibrantType(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,
fibrant-type: FibrantType(X),
csm-fibrant-type: csm-fibrant-type(G;H;s;FT),
subtype_rel: A ⊆r B
Lemmas referenced :
csm-ap-type_wf,
csm-composition_wf,
composition-op_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
fibrant-type_wf,
cube_set_map_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
dependent_pairEquality_alt,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
universeIsType,
instantiate,
applyEquality,
inhabitedIsType
Latex:
\mforall{}[G,H:j\mvdash{}]. \mforall{}[s:H j{}\mrightarrow{} G]. \mforall{}[FT:FibrantType(G)]. (csm-fibrant-type(G;H;s;FT) \mmember{} FibrantType(H))
Date html generated:
2020_05_20-PM-05_20_25
Last ObjectModification:
2020_04_12-AM-08_43_38
Theory : cubical!type!theory
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