Nuprl Lemma : csm+_wf+
∀[H,K:j⊢]. ∀[A:{H ⊢ _}]. ∀[tau:K ij⟶ H]. ∀[B:{H.A ⊢ _}]. (tau++ ∈ K.(A)tau.(B)tau+ ij⟶ H.A.B)
Proof
Definitions occuring in Statement :
csm+: tau+,
cube-context-adjoin: 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
Lemmas referenced :
csm+_wf,
cube-context-adjoin_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
csm-ap-type_wf,
cubical-type_wf,
cube_set_map_wf,
cubical_set_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
instantiate,
applyEquality,
because_Cache,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
universeIsType,
inhabitedIsType
Latex:
\mforall{}[H,K:j\mvdash{}]. \mforall{}[A:\{H \mvdash{} \_\}]. \mforall{}[tau:K ij{}\mrightarrow{} H]. \mforall{}[B:\{H.A \mvdash{} \_\}]. (tau++ \mmember{} K.(A)tau.(B)tau+ ij{}\mrightarrow{} H.A.B)
Date html generated:
2020_05_20-PM-01_58_39
Last ObjectModification:
2020_04_09-AM-10_53_58
Theory : cubical!type!theory
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