Nuprl Lemma : csm-ap-term-subset-subset
∀[Gamma,K:j⊢]. ∀[s:K j⟶ Gamma]. ∀[phi:{Gamma ⊢ _:𝔽}]. ∀[psi:{Gamma, phi ⊢ _:𝔽}]. ∀[A:{Gamma, phi, psi ⊢ _}].
∀[Z:{Gamma, phi, psi ⊢ _:A}].
((Z)s ∈ {K, (phi)s, (psi)s ⊢ _:(A)s})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
csm-ap-term: (t)s,
cubical-term: {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-ap-term-subset,
context-subset_wf,
csm-ap-term_wf,
face-type_wf,
csm-face-type,
context-subset-map,
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
cubical-type_wf,
cube_set_map_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
universeIsType,
instantiate,
applyEquality,
inhabitedIsType
Latex:
\mforall{}[Gamma,K:j\mvdash{}]. \mforall{}[s:K j{}\mrightarrow{} Gamma]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. \mforall{}[psi:\{Gamma, phi \mvdash{} \_:\mBbbF{}\}].
\mforall{}[A:\{Gamma, phi, psi \mvdash{} \_\}]. \mforall{}[Z:\{Gamma, phi, psi \mvdash{} \_:A\}].
((Z)s \mmember{} \{K, (phi)s, (psi)s \mvdash{} \_:(A)s\})
Date html generated:
2020_05_20-PM-02_57_40
Last ObjectModification:
2020_04_06-AM-11_18_56
Theory : cubical!type!theory
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