Nuprl Lemma : context-subset-1
∀[Gamma:j⊢]. {Gamma, 1(𝔽) ⊢ _} ≡ {Gamma ⊢ _}
Proof
Definitions occuring in Statement :
context-subset: Gamma, phi,
face-1: 1(𝔽),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
ext-eq: A ≡ B,
and: P ∧ Q,
member: t ∈ T,
uimplies: b supposing a
Lemmas referenced :
subset-cubical-type,
context-subset_wf,
face-1_wf,
context-1-subset,
subset-context-1,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
instantiate,
because_Cache,
universeIsType
Latex:
\mforall{}[Gamma:j\mvdash{}]. \{Gamma, 1(\mBbbF{}) \mvdash{} \_\} \mequiv{} \{Gamma \mvdash{} \_\}
Date html generated:
2020_05_20-PM-02_54_18
Last ObjectModification:
2020_04_04-PM-05_08_42
Theory : cubical!type!theory
Home
Index