Nuprl Lemma : fibrant-type-cumulativity
∀[X:j⊢]. (FibrantType(X) ⊆r fibrant-type{i':l}(X))
Proof
Definitions occuring in Statement :
fibrant-type: FibrantType(X),
cubical_set: CubicalSet,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
member: t ∈ T,
fibrant-type: FibrantType(X)
Lemmas referenced :
cubical-type-cumulativity,
composition-op_wf,
cubical_set_cumulativity-i-j,
cubical-type-cumulativity2,
fibrant-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaEquality_alt,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairEquality_alt,
cut,
hypothesisEquality,
applyEquality,
introduction,
extract_by_obid,
isectElimination,
hypothesis,
sqequalRule,
universeIsType,
instantiate
Latex:
\mforall{}[X:j\mvdash{}]. (FibrantType(X) \msubseteq{}r fibrant-type\{i':l\}(X))
Date html generated:
2020_05_20-PM-05_20_10
Last ObjectModification:
2020_04_12-AM-08_50_24
Theory : cubical!type!theory
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