Nuprl Lemma : composition-structure_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. (Gamma ⊢ Compositon(A) ∈ 𝕌{[i' | j'']})
Proof
Definitions occuring in Statement :
composition-structure: Gamma ⊢ Compositon(A),
cubical-type: {X ⊢ _},
cubical_set: CubicalSet,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
composition-structure: Gamma ⊢ Compositon(A),
prop: ℙ
Lemmas referenced :
composition-function_wf,
uniform-comp-function_wf,
cubical-type_wf,
cubical_set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
setEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate
Latex:
\mforall{}[Gamma:j\mvdash{}]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. (Gamma \mvdash{} Compositon(A) \mmember{} \mBbbU{}\{[i' | j'']\})
Date html generated:
2020_05_20-PM-04_22_16
Last ObjectModification:
2020_04_11-PM-05_08_15
Theory : cubical!type!theory
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