Nuprl Lemma : csm+-comp-csm+-interval
∀[H,K,X:j⊢]. ∀[tau:K j⟶ H]. ∀[s:X j⟶ K]. (tau+ o s+ = tau o s+ ∈ X.𝕀 j⟶ H.𝕀)
Proof
Definitions occuring in Statement :
interval-type: 𝕀,
csm+: tau+,
cube-context-adjoin: X.A,
csm-comp: G o F,
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
csm-comp: G o F,
csm+: tau+
Lemmas referenced :
csm+-comp-csm+-sq-interval,
csm+_wf_interval,
csm-comp_wf,
cube_set_map_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :memTop,
hypothesis,
hypothesisEquality,
universeIsType,
because_Cache,
inhabitedIsType,
instantiate
Latex:
\mforall{}[H,K,X:j\mvdash{}]. \mforall{}[tau:K j{}\mrightarrow{} H]. \mforall{}[s:X j{}\mrightarrow{} K]. (tau+ o s+ = tau o s+)
Date html generated:
2020_05_20-PM-02_38_18
Last ObjectModification:
2020_04_21-PM-00_01_22
Theory : cubical!type!theory
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