Nuprl Lemma : csm-subtype-iso-instance1
∀[X,H:j⊢]. ∀[phi:{H ⊢ _:𝔽}]. (X j⟶ H.𝕀, (phi)p ⊆r X j⟶ H, phi.𝕀)
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-type: 𝔽,
interval-type: 𝕀,
cc-fst: p,
cube-context-adjoin: X.A,
csm-ap-term: (t)s,
cubical-term: {X ⊢ _:A},
cube_set_map: A ⟶ B,
cubical_set: CubicalSet,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a
Lemmas referenced :
cube-context-adjoin_wf,
interval-type_wf,
context-subset_wf,
csm-subset-codomain,
csm-ap-term_wf,
face-type_wf,
csm-face-type,
cc-fst_wf,
context-adjoin-subset1,
cubical-term_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
Error :memTop,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
universeIsType,
inhabitedIsType
Latex:
\mforall{}[X,H:j\mvdash{}]. \mforall{}[phi:\{H \mvdash{} \_:\mBbbF{}\}]. (X j{}\mrightarrow{} H.\mBbbI{}, (phi)p \msubseteq{}r X j{}\mrightarrow{} H, phi.\mBbbI{})
Date html generated:
2020_05_20-PM-03_05_52
Last ObjectModification:
2020_04_06-PM-07_34_51
Theory : cubical!type!theory
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