Nuprl Lemma : context-subset-subtype-and
∀[Gamma:j⊢]. ∀[phi1,phi2:{Gamma ⊢ _:𝔽}]. ({Gamma, phi1 ⊢ _} ⊆r {Gamma, (phi1 ∧ phi2) ⊢ _})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-and: (a ∧ b),
face-type: 𝔽,
cubical-term: {X ⊢ _:A},
cubical-type: {X ⊢ _},
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,
subtype_rel: A ⊆r B
Lemmas referenced :
subset-cubical-type,
context-subset_wf,
face-and_wf,
face-term-implies-subset,
face-term-and-implies1,
cubical-term_wf,
face-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
instantiate,
because_Cache,
sqequalRule,
axiomEquality,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[phi1,phi2:\{Gamma \mvdash{} \_:\mBbbF{}\}]. (\{Gamma, phi1 \mvdash{} \_\} \msubseteq{}r \{Gamma, (phi1 \mwedge{} phi2) \mvdash{} \_\})
Date html generated:
2020_05_20-PM-02_52_34
Last ObjectModification:
2020_04_04-PM-05_07_02
Theory : cubical!type!theory
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