Nuprl Lemma : context-subset-term-subtype
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[phi:{Gamma ⊢ _:𝔽}]. ({Gamma ⊢ _:A} ⊆r {Gamma, phi ⊢ _:A})
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
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,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
subtype_rel_transitivity,
cubical-term_wf,
cubical-type-cumulativity2,
cubical_set_cumulativity-i-j,
context-subset_wf,
face-1_wf,
thin-context-subset,
subset-cubical-term,
face-type_wf,
cubical-type_wf,
cubical_set_wf,
subset-context-1,
face-term-implies-subset,
face-term-implies-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[phi:\{Gamma \mvdash{} \_:\mBbbF{}\}]. (\{Gamma \mvdash{} \_:A\} \msubseteq{}r \{Gamma, phi \mvdash{} \_:A\})
Date html generated:
2020_05_20-PM-02_55_24
Last ObjectModification:
2020_04_06-AM-10_25_56
Theory : cubical!type!theory
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