Nuprl Lemma : csm+_wf_interval
∀[H,K:j⊢]. ∀[tau:K j⟶ H]. (tau+ ∈ K.𝕀 j⟶ H.𝕀)
Proof
Definitions occuring in Statement :
interval-type: 𝕀,
csm+: tau+,
cube-context-adjoin: X.A,
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,
interval-type_wf,
csm-interval-type,
cube_set_map_wf,
cubical_set_wf,
cube-context-adjoin_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
Error :memTop,
universeIsType,
inhabitedIsType,
lambdaEquality_alt
Latex:
\mforall{}[H,K:j\mvdash{}]. \mforall{}[tau:K j{}\mrightarrow{} H]. (tau+ \mmember{} K.\mBbbI{} j{}\mrightarrow{} H.\mBbbI{})
Date html generated:
2020_05_20-PM-02_38_08
Last ObjectModification:
2020_04_20-AM-10_13_17
Theory : cubical!type!theory
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